Math Central - mathcentral.uregina.ca
Quandaries & Queries
Q & Q
. .
topic card  



list of
. .
start over

162 items are filed under this topic.
A 50:1 ratio in a pint 2020-05-22
From Steve:
How much oil do I need to put in a pint if it's 50:1 ratio
Answered by Harley Weston.
Is there an equation to find what percent of 0 is 1? 2020-03-09
From Asher:
Question: Is there an equation to find what percent of 0 is 1.

I remember learning quite a long time ago that the answer inst 0 and it isn't infinity. I'm pretty sure it was something like %=0 approaching infinity or %=1 approaching infinity. And I know it depends what value you assign the numbers i.e. dollars or temperature. Furthermore, is asking "what percent 1 dollar is of 0 dollars" the same question as "what percent profit do you make from selling something worth 0 dollars for 1 dollar."

Thank you for your time and consideration -Asher

Answered by Penny Nom.
30% profit 2020-02-20
From Sidra:
A car dealer bought a car for £7500 and sold it for 30% profit.

For how much did he sell the car?

Answered by Penny Nom.
Arranging 10 digits 2019-10-09
From Laxmi:
1)The integers 0 to 9 are arranged along a straight line in some order.a) find a possible arrangement in which the sum of any three adjacent numbers is less than 15.b)is there an arrangement of this kind 0 is not included in the numbers.
Answered by Penny Nom.
400 in 7.5 billion 2019-08-28
From Emma:
What is a better way to express 400 in 7.5 billion? My daughter has a rare condition, I want to know the answer to say “she is 1 in a ...”
Answered by Penny Nom.
Six digit numbers from 4 digits 2019-07-30
From Tab:
How many six digit combinations can be made from the numbers zero, two, five, eight? With repetition of numbers
Answered by Penny Nom.
One part in 10^x 2019-06-26
From Jim:
What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “...to within one part in 10x.”
Answered by Penny Nom.
The perimeter of 200 acres 2019-06-14
How many feet is the perimeter of 200 acres?
Answered by Penny Nom.
An 80 acre square 2019-05-11
From Linda:
How long and wide is an 80-acre piece of land that is square?
How long and wide is a 160-acre piece of land that is square?

Answered by Penny Nom.
Four multiples of 10 2017-09-23
From Laudacir:
Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be?
Answered by Penny Nom.
A 4 sided lot 2017-08-15
From Micheal:
If one side of .4 acre is 25 feet what would the other three sides be
Answered by Penny Nom.
Factorials 2017-07-27
From dinesh:
Is there any shortcut formula for multiply series numbers. like
1x2x3x4x5.......x100 =?

Answered by Penny Nom.
A 40 acre square 2017-05-14
From Richard:
How many feet on each side of 40 acre square ?
Answered by Penny Nom.
A circle inscribed in a 30-6-90 triangle 2017-04-07
From Kameron:
i have been given a problem with a 30-60-90 triangle and a circle inscribed with a radius of 2 and was told to find the perimeter of the triangle
Answered by Penny Nom.
2^a, 2^b, 1^1 and 1^0 2017-03-17
From Émile:
If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0?
Answered by Penny Nom.
980 cubic yards of dirt 2016-12-17
From Jondi:
I am trying to visualize 980 cubic yards of dirt by using a metaphor.
Would this be the size of a car?
A fire engine?
A semi-trailer?
How many trucks would you need to haul away 980 yards of dirt?

Answered by Penny Nom.
y = mx + c and Ax + By + C = 0 2016-10-18
From Erick:
please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o form.
Answered by Penny Nom.
The diagonal of a 10 acre square 2016-04-11
From Derrick:
I own 100 acre square of land. I want to run from farthest corner of property to farthest corner, Diagonally. How many miles would I have traveled?
Answered by Penny Nom.
20 mangoes 2016-04-01
From Mussharat:
I have 20 mangoes and have to put them in 5 boxes such that the numbers will be odd numbers.Also I can't cut or take the seed out from the mango . What should I do. It's really confusing.
I'll be more than happy if you could help me.

Answered by Penny Nom.
0/0 2016-02-14
From Noni:
Q. 0÷0=1 Why it is wrong when 4÷4=1; 3÷3=1; 2÷2=1: 1÷1=1 ?
Answered by Penny Nom.
20 golfers playing a 20 week season 2015-12-07
From Jeff:
We have 20 golfers playing a 20 week season. We play in foursomes. How best to set foursomes so everyone can play with every without playing with the same person multiple times?
Answered by Victoria West.
A six team league to play a 20 game schedule 2015-10-19
From Kelly:
Hi there. Some of your posts are close, but my problem is evening out the home and away games. We have 6 teams in our league and we are going to play a 20 game schedule, playing everyone 4 times. We will play Fridays and Saturdays, each weekend. Of course the ideal would be to have each team have a home and an away game each weekend, but I realize that is impossible, but I would like it as close as possible. Any help would be much appreciated!! We also were considering opening with a home and away - Friday then Saturday with the same teams. Then carrying on with playing everyone else and then possibly finishing up with the same home and home
Answered by Victoria West.
How can the probability be zero? 2015-10-13
From anagha:
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing. Most of'em say that there are infinite number of points on the circumference. and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...?

Answered by Harley Weston.
Mathematics 2015-10-13
From anagha:
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing. Most of'em say that there are infinite number of points on the circumference. and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...?

Answered by Harley Weston.
20 golfers for 6 days 2015-09-11
From Dave:
have 20 golfers for 6 days. Each player should pair with 18 golfers used a system on your website which is good for 5 days, but cannot get the 6th day. Thanks for your help Dave
Answered by Victoria West.
20 golfers playing four rounds 2015-08-17
From Paul:
I have a party of 20 golfers playing four rounds in fourballs. I realise that everyone will have 7 players that they do not play with, however I want to ensure that no one plays with the same person twice and that the Captain plays with the 12 players of his choice.
Answered by Victoria West.
n^2 is a multiple of 100 2015-03-30
From Rahul:
I have to prove that n^2 is a multiple of 100 is necessary or Sufficient condition (or both) for n being multiple of 10
Answered by Penny Nom.
What is 1000 billion billion? 2015-03-10
From LeRoy:
what does this mean? 1000 billion billion
Answered by Penny Nom.
How many square feet in 10 gallons of liquid at 1/4 in thick? 2014-11-14
From Rich:
How many square feet in 10 gallons of liquid at 1/4 in thick
Answered by Penny Nom.
A 10-foot piece of PVC pipe 2014-10-21
From David:
A plumber has a 10-foot piece of PVC pipe. How many 9/5-foot pieces can be cut from the 10-foot piece ?
Answered by Penny Nom.
211(base x)=152(base 8) 2014-09-09
From Vaidehi:
Find the base value (i.e. x):
211(base x)=152(base 8)

Answered by Penny Nom.
Golf for 10 2014-08-12
From Fred:
We have 10 golfers playing 4 rounds: one 4-some and two 3-somes each round. Can you suggest the best distribution of players?
Answered by Victoria West.
20 teams and 10 competition stations 2014-06-04
From Joel:
I have 20 teams. There are 10 competition stations. Each station will accommodate exactly 2 teams to compete with each other at a time.

Each of the 20 teams needs to compete at each of the 10 stations exactly one time.

Here's the catch I cannot solve: how to schedule it so that each team plays EVERY OTHER TEAM once and only once, while never repeating a station.

Answered by Victoria West.
10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball 2014-06-04
From adrian:
Hi, We are off to Scotland on our yearly golfing trip soon. Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball. I would like to ensure that each golfer plays with the other guys an equal amount of times, guess 3ish? and we share the amount of times each player plays in the 4ball. Hope you can help?
Answered by Victoria West.
The combination of 6 numbers from 1 to 355 that gives us 360 2014-05-29
From Ion:
My name is Ion and I am trying to find the number of combinations of 6 numbers (angles) that would sum to 360 (degrees).

Thank you!

Answered by Robert Dawson.
A schedule for 2 teams of 10 2014-05-07
From John:
How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 1-10, Team B would consist of players 11-20. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!!
Answered by Victoria West.
Golf with 3 teams of 20 2014-04-21
From Joshua:
Thank in advance for this great service

Golf - new - 3 teams of 20 - to create 20 unique groups of 3

For example use 3 teams of 3

1a 2a 3a
1b 2b 3b
1c 2c 3c

So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c

Groups can only have one a, one and one c - and that combo should be unique

Answered by Victoria West.
A golf league with 20 players over 17 weeks 2014-04-12
From Chris:
I have a golf league 20 players and 17 weeks. We don't have teams so I just want to have everyone to play with each other the about same number of time and, hopefully, randomly distributed throughout the season. We have had situations in the past where two people play together for three weeks in a row and then not anymore for the rest of the season. From other posts, I see how to schedule the first 5 weeks without repeats but I can’t figure out an algorithm to for the rest of the season. Thanks!
Answered by Victoria West.
Golf with 20 players and one compulsory bye 2014-03-31
From Wayne:
I'm trying to run an event with 20 players, I would like if at all possible to limit amount of people playing repetitively together. (Mix it up and play with different people). Here's the conditions. I want groups of 4 over 5 rounds. On each round I want 4 players to drop out and have a bye (to help run the game) but I dont want them helping a group they've played in if I can help it. Is this possible ?
Answered by Victoria West.
Counting in base five using words not digits 2014-01-25
From Randy:
We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure - in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow - how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems?
Answered by Harley Weston.
Scheduling 10 people for 5 rounds 2013-11-20
From Keith:
Using golf as an example, I would like to schedule 10 people for 5 rounds with 2 groups of 4 and 1 twosome each round. I would like to minimze the number of times any one player plays with another. Can you provide an optimal schedule? Thank you for your help.
Answered by Victoria West.
8 numbers from 80 2013-09-04
From susan:
Out of 80 numbers how many combinations of 8 are there and what are they.
Answered by Penny Nom.
More than half of the people said... 2013-08-26
From Lucy:
The question is:
Samoa 23%
Brazil 41%
Sri Lanka 52%
Senegal 39%
Armenia 37%
Croatia 20%
Why is the following statement true for the data above: More than half of the people said they were interested in Sri Lanka. The reason I don't understand the problem is that because the percentages add up to be greater than 100%, that means that the 500 people(as stated in the question) who participated in the survey got to pick more than once. Therefore, it is not 52% out of 100% anymore. Thanks for taking the time to answer my question.

Answered by Robert Dawson.
10 guys playing 8-9 hole rounds 2013-07-19
From Jason:
I have 10 guys playing 8 9 hole match-play rounds. I need to have everybody play the other 9 men, but need to limit them to only a 9 hole match between them. If we need to go 3-3-4 or 2-4-4 for a better solution, that may be possible.
Answered by Victoria West.
20 golfers over 5 days 2013-05-09
From Russ:
we have 20 golfers over 5 days, with 4 people per foursome which makes 5 groups each day. I would like to each person to play with everyone at least once if possible. Do you have a formula for this?
Answered by Victoria West.
10 golfers playing four rounds 2013-04-09
From Terry:
I've searched "golf" and "golf 10" but don't see 10 golfers playing four rounds (each round having one foursome plus two threesomes, and no "flights" as in one earlier answer); each player playing at least once with a maximum number of the other nine over the four rounds?
Answered by Victoria West.
100 animals 2013-02-25
From Jessica:
You have exactly $100.00 to spend. You must get 100 animals.
The chicks cost $0.10 each.
The pigs cost $2.00 each.
The sheep cost $5.00 each.
You must get some of each animal.
How many of each animal can you get?

Answered by Penny Nom.
We have 10 golfers and four rounds of golf in two days 2013-02-05
From Steve:
We are having a golf tournament. We have 10 golfers and four rounds of golf in two days. We are going to break the group of 10 into two flights. Flight A and Flight B. We would like all members in Flight A to play one nine hole match against each other. All players in Flight B to play one nine hole match against each other. Could we play in groups of 4,3 and 3? What is the best way to make the pairings work?
Answered by Robert Dawson.
Golf for 20, two teams of 10 2012-08-30
From Mark:
Hi I have to teams of 10 people playing Ryder cup format(against each other) Can I have all 20 people playing with someone different over 3rounds of golf while remaining on there respective team I.e. players 1 to 10 must team up with a player of that group against a pair for players 11 to 20
I hope you can solve this for me
Thanks a bunch Mark

Answered by Victoria West.
Expanded exponential form? 2012-06-12
From Ramon:
express the numbers 990 614 000 005 in expanded exponential form.
Answered by Harley Weston.
Golf for 10 2012-04-18
From Bob:
Question from Bob:

I am trying to set up pairings for 4 rounds of golf with only 10 golfers (2 foursomes and 1 twosome) and trying to minimize duplications. Any formulas or help?

Answered by Victoria West and Harley Weston.
240 acres 2012-02-17
From jon:
How many linear feet are in a 240 acre rectangle piece of property
Answered by Harley Weston.
Expressing 0.5% 2012-02-06
From Kenneth:

It is correct to express 0.5% as 5 tenths of one percent.

Is it also correct to express 0.5% as 5 tenths of one-hundred percentage points or 5 tenths of one percentage point?

I think it would be 5 tenths of one percentage point because 5 tenths of one-hundred percentage points would be 50 percentage points, but I'm not sure.

I thank you for your reply.

Answered by Penny Nom.
Converting from base 4 to base 10 2011-11-29
From anjg:
How to convert base 4 number 2^11 to base 10 number?
Answered by Penny Nom.
1 divided by 0 and infinity 2011-10-24
From ritika:
we say that one divided by zero gives us infinity, then why zero multiplied by infinity does not gives us one?????????????
Answered by Robert Dawson.
Expanded form 2011-10-12
From Chris:
Write this number in expanded form
4 326 180 501


Answered by Penny Nom.
A group of 40 golfers 2011-07-11
From Doug:
We are a group of 40 golfers who play in 10 x foursomes playing 3 rounds. Can we all play with different players each round yet maintain the foursomes format.
Answered by Victoria West.
Construct a 30 degree angle 2011-06-10
From Ella:
they give you a simple straight line and ask you to construct an angle of 30 degrees at one end of the line using only a ruler and a compass?
Answered by Penny Nom.
Arrangements of ten letters 2011-04-15
From Mustafa:
In how many ways can the ten letters of the word GELATINOUS be arranged in a line so that the vowels are in alphabetical order (not necessarily together) when read from left to right?
Answered by Penny Nom.
A golf league of 60 golfers 2011-04-14
From Keith:
I have a golf league of 60 golfers and I want to have each golfer play in a different group of 4 each week for 24 weeks. How can I do this
Answered by Victoria West.
What is x to the power of 0? 2011-03-23
From Jason:
What is x to the power of 0?
Answered by Robert Dawson.
20 acres, 12 inches deep 2011-02-24
From David:
How many linear yards of material is needed for a square plot of 20 acres by 12 inches deep?
Answered by Penny Nom.
1/0 and 2/0 2011-02-11
From Dixit:
How are the infinite number obtained by dividing 1 / 0 and 2 / 0 are different?
Answered by Penny Nom.
10 golfer playing 5 rounds 2011-01-09
From Jeff:
need pairing for 10 golfer playing 5 rounds of golf.
Answered by Victoria West.
The new diameter is 50 per cent larger than the original. 2010-09-04
From mahwish:
. A circular logo is enlarged to fit the lid of a jar. The new diameter is 50 per cent larger than the original. By what percentage has the area of the logo increased?
Answered by Tyler Wood.
Does 1= 0.9999....? 2010-04-07
From Asia:
Does 1= 0.9999....? There seems to be different opinions on this.
Answered by Robert Dawson.
The sides of a 30-60-90 triangle 2010-03-29
From maris:
Find the sides of a 30-60-90 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables.
Answered by Penny Nom.
An isosceles triangle 2010-02-11
From Kim:
I am given the length of the two legs of an isosceles triangle (8), and the base angles are 30 degrees...I am asked to find the area of the triangle with only this information
Answered by Tyler Wood.
A cylinder is cut at an angle of 20 degrees 2010-01-25
From sanjay:
If I have a cylinder with 40mm diameter and I will cut it at an angle 20 degrees so what would be the increased radius or dia.??? of the cylinder
Answered by Penny Nom.
Bases larger than ten 2009-12-14
From Nick:
For numbers in bases larger than ten, what are the digits by mathematicians' conventions?

I assume the first 10 are always 0-9. I know two computer science conventions (for hexadecimal (A-F case-insensitively) and for base 85 (case-sensitivity plus 23 other characters)) and as a school student I learned that base 12 uses either T and E (which confused me when I thought they stood for Eleven and Twelve) or A and B, the latter as capitals only. Clearly, these conventions are in conflict.

I saw your reply in http://mathcentral.uregina.ca/QQ/database/QQ.09.99/magin1.html as accessed a few minutes ago but hope that in the 10 years since then mathematicians have arrived at a convention. Have they?
Thank you.


Answered by Claude Tardif.
10 golfers 2009-09-06
From Bill:
We have 10 golfers scheduled to play over five days on vacation in November. Each day we will play in three groups of three and one foursome. Is there an optimum solution that would assure that every golfer plays with every other golfer at least once while no golfer plays an inordinate number of times with any other golfer or too often in a foursome?
Answered by Victoria West.
30 students 2009-08-06
From Peter:
Question from Peter, a student:

Can you please help with the following questions?

(a) It is known that among any group of the three students in a class two of them are friends. Total number of students is 25. Prove that there is a student who has at least 12 friends.

(b) There are 30 students in a class. They sit at 15 double desks, each one is for two students. Half of the girls sit with boys. Is it possible to make a rearrangement so that half of the boys sit with girls?

Answered by Penny Nom.
The sum of the angles of a triangle 2009-05-18
From mary:
prove that the sum of the three angles inside any triangle always add up to 180 degrees?
Answered by Harley Weston.
0123456789 2009-03-25
From Dr.:
Many years ago I discovered that there are 33 numbers which, when multiplied by 0123456789, simply rearrange the digits. Surprisingly (to me at least) is the fact that the digits of all of those 33 numbers add up to one of the 6 "cardinal" numbers 1, 2, 4, 5, 7, and 8. For example 6 + 2 = 8 and 62 X 0123456789 = 7654320918 etc.
Another interesting (to me) fact is that only the cardinal numbers 1, 2, 4, 5, 7, and 8 rearrange the digits in the number 9876543210.
My question is: "Is this known to anyone but me and the people I have told?"

Answered by Robert Dawson.
A shape with 10 sides 2009-03-03
From Sandra:
One of my son's math questions is as follows: Suppose I have a shape with 10 sides. I choose a vertex then draw lines to the other vertices that dont share sides with the first vertex. How many vertices will that be and why?
Answered by Penny Nom.
0/0 and 1/0 2009-02-16
From Justin:
I was just wondering which is bigger 0/0 or 1/0?


Answered by Robert Dawson and Harley Weston.
0/0 2009-02-15
From Justin:
Hello, I was just wondering, what is the difference between 0/0 being represented as nullity or as an indeterminate form?


Answered by Harley Weston.
A 30-60-90 triangle 2009-02-03
From Inez:
If you have a 30-60-90 triangle and the only side you get is 73 and a 90 degree box, how do you find the area?
Answered by Penny Nom.
20 of us golf together in groups of 4 2009-01-24
From D.:
Every Sunday, 20 of us golf together in groups of 4. I am looking for a way that each of us play with 3 other people each week and ultimately get to play in groups that are unique. For instance if week 1, I play with 2, 3, 4 and then the next week I play with 5, 6, 7, and the 3rd week I play with 8, 9, 10 and so forth until I have played with everyone. Everbody else should be doing the same thing. Can you give me a schedule for this and how many weeks would it take for all of us to accomplish this where we all play with different combinations of people. (We should not play with the same person very often or even the same pairs of people but everyone should play with everybody else) I hope this makes sense........whew and thanks!
Answered by Victoria West.
What is one trillion divided by 10? 2008-12-09
From mark:
can you please tell me what one trillion divided by 10 is
Answered by Robert Dawson and Penny Nom.
0.99999.... 2008-09-23
From Eve:
Hi, i had a problem with change 0.99999... this recurring decimal to a fraction. I know the method, but the answer I got is 1 as you can see below.

Where have i done wrong?

Answered by Harley Weston.
Aboriginal number groupings 2008-09-04
From Barbara:
Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently?
Answered by Harley Weston.
20 golfers playing 5 rounds in 4-somes 2008-09-03
From joe:
20 golfers playing 5 rounds in 4-somes. 5 players in group A play with all 15 golfers in groups B,C,D but not with any in their own group (A). 5 players in group B play with all 15 players in groups A,C,D but not with any in their own group (B) and so on. So each 4-some has an A,B,C,&D player each of the 5 rounds.
Answered by Chris Fisher.
A 10 acre square 2008-05-12
Answered by Penny Nom.
Zero divided by infinity 2008-05-03
From ANNE:
There was a question about what do you get when you divide Zero by infinity. There was an example using Potatoes. Could someone please explain a little bit more in detail, so that I can help my son who has Schizophrenia understand. He is big into Mathematics and is consumed by this question. Thankyou so much, Anne
Answered by Penny Nom.
Division by zero 2008-05-01
From Bill:
Why does multiplication have a favored status so as to make division by zero undefined?
Answered by Harley Weston.
A 30-60-90 triangle 2008-04-16
From Ron:
30-60-90 triangle. Base is 2.75 how do I find the length of the other two sides?
Answered by Penny Nom.
A 100 acre square pasture 2008-04-03
From Richard:
I need to know how many lineal feet there is around a 100 acre pasture that is square in shape. I am no longer able to get out and measure it myself, and cannot remember the math to compute it.
Answered by Penny Nom.
Twenty golfers 2008-03-16
From john:
I have a group of 20 golfers. We plan on playing 6 rounds of golf in 4 days. I would like to have the most possible combinations of players without each player playing with anyone if possible, in the 4 days of golf
Answered by Victoria West.
The product of two numbers is 1,000,000,000 2008-03-14
From Henry:
What two numbers that don't in zero when multiplied equals 1,000,000,000 and same with 1,000,000,000,000,000,000.
Answered by Penny Nom.
Choosing 10 numbers from 40 numbers 2008-01-18
From Antwan:
I have 40 numbers........number 1-40. I want to know how many times i can chose 10 of those numbers without picking the same exact sequence twice if its even possible?
Answered by Stephen La Rocque.
Multiplying numbers in bases other than 10 2008-01-08
From Imaiya:
In class we've been learning about numbers with a base other than ten. For example, base 7, base 5, and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10. I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.

Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42 Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78

If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much, and once again, thank you for your great site!

Answered by Stephen La Rocque.
Base 10 to base 5 2007-10-09
From Angela:
I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a step-by-step instruction on how to do this?
Answered by Stephen La Rocque.
Golf pairings 2007-10-02
From Mike:
Regarding arranging golf players so no person plays with anyone more than once. You have given examples for 16 and 24 players. If it can be done, i need a solution for 20 players, 4 players per team one round per day for 5 days
Answered by Victoria West.
If A is 1 and Z is 26 2007-06-29
From Sue:
If A is 1 and Z is 26 is there a word that when you multiply all the numbers instead of letters adds up to a million?
Answered by Chris Fisher and Harley Weston.
How can we explain to middle school students that 0^0=1? 2006-10-15
From Peter:
How can we explain to middle school students that 0^0=1?
Answered by Steve La Rocque, Penny Nom, Claude Tardif and Harley Weston.
a _________________ line forms a 90 degree angle with another line 2006-09-24
From Lisa:
a _________________ line forms a 90 degree angle with another line is this to it what fills in the blank? first letter is E third letter is R and has 13 letters
Answered by Stephen La Rocque.
A base number raised to the power of 0 2006-08-24
From Sheila:
I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out.
Answered by Penny Nom.
Twenty golfers 2006-05-08
From Mona:
We have twenty golfers and four rounds of golf. We would like to figure out how to make foursomes so that each golfer plays with as many different golfers as possible.
Answered by Penny Nom.
Interest computed on a 360 per year basis 2006-04-06
From Sonya:
Okay, I am reading this promissory note that says interest is computed on 365/360 basis by applying the ratio of annual interest rate (24%) over a year of 360 days. I sure do not remember anything like this in school, and am stumped.
Answered by Stephen La Rocque.
A triangle of 50p pieces 2006-02-22
From Stuart:

Ok, so i am collecting 50p pieces and arranging them on my desk in the shape of a triangle.
50p 50p
50p 50p 50p
50p 50p 50p 50p

I want to work out how much money I'm saving just by knowing how many rows of coins there are. If i can work out how many coins there are just by knowing how many rows I have I can just divide by 2 to find out the amount in dollars.

Answered by Penny Nom.
Is a zero considered an even or odd number? 2005-12-13
From Sylvia:
Is a zero considered an even or odd number?
Answered by Penny Nom.
A 30-60-90 triangle 2005-09-11
From Gary:
I have the length of only 1 side of triangle with angles of 30-60-90 degrees. How can I find the length of the other 2 sides?
Answered by Penny Nom.
0.999..., asymptotes and infinity 2004-12-17
From Mike:
My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!!
Answered by Claude Tardif and Harley Weston.
A 30-60-90 triangle 2004-11-09
From Amy:
How do you find the length of the hypotenuse of a 30-60-90 triangle when the side opposite the 60 degree angle is 6 inches?
Answered by Penny Nom.
20 Golfers 2004-10-26
From Ian:
I have 20 golfers playing over 6 days I would like to schedule all 20 golfers in 5 groups of 4 on each day here is the catch.... I would like each player to play with each other once during the 6 days.
Answered by Chris Fisher.
Zero to the zero 2004-09-18
From Greta:
My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified.
Answered by Penny.
The "22" puzzle and the "1089" puzzle 2004-04-22
From Marcelle:

1. Choose 3 digits from 1-9
2. Make all the 2 digit numbers you can from these (6)
3. Add the 3 original digits and divide them into the sum from step 2.
The answer is always '22'. I just can't understand why. Can you please help.

Another one related to this is it:
1. Choose a three digit number ensuring the first and third digit are differnt by at least two.
2. Make the reverse three digit number and subtract the smaller one from the larger of these.
3. Take this answer and reverse it and add these two 3 digit numbers .

643 - 346 = 297
297 + 792 = 1089

it doesn't matter what numbers are used, the results are alwasy the same. eg 22 or 1089

Answered by Paul Betts.
Zero 2004-02-12
From Syazwan:
can you tell me who and when the number zero was discoveredd
Answered by Penny Nom.
1/0 = ?? 2003-12-09
From Lisa:
One of my students asked me a fractions question. She knows that 0/1 equals 0 but does 1/0 also equal 0?
Answered by Walter Whiteley and Penny Nom.
10,000 2003-10-08
From Nathan:
what two numbers make the product of 10,000. Neither number can end in a zero
Answered by Penny Nom.
0/0 2003-09-25
From Thomas:
How is 0/0 ever defined.
Answered by Penny Nom.
Converting from base 10 to base 5 2003-09-10
From Susy:

My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5.

His first question of:

24(10) he has calculated to be 4x5 + 4x1 = 44 (5)

The next question however is the tricky one.Ý We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it.

25 (10) = _________________ 100 (5)

Can you help us figure out how we reach the answer.

Answered by Claude Tardif and Penny Nom.
Positive, negative and zero 2003-09-04
From Brian:
Can the Value of zero be positive or can it be negative or can it be both.
Answered by Penny Nom.
Converting to base 10 2003-08-28
From Karen:
My son is in 5th grade.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý Can you explain it to me in the simplest terms?
Answered by Penny Nom.
Division by zero 2003-01-19
From David:
I've been to your site and am interested on the subject of division by 0. It's easy enough to give answers, but it's very hard, especially in this case, to make someone understand a mathematical problem.

It's been about a year since my Calc class, and we never went over division by 0, only infinite numbers and such. My question is: How would you work a problem of (real number) / 0 ? As ignorant as it may sound to you, I am having trouble grasping this since I've only begun to understand some of it. Perhaps you could help.

Answered by Harley Weston.
Exponent 0 2002-10-02
From Debbi:
can you please tell me what the exponent 0 is (i.e. 70)
Answered by Penny Nom.
0.99999... 2002-09-26
From Erica:
Yesterday in my 8th grade math class we were being taught how to convert a Repeating Decimal into a fraction. Since I, for some odd reason, seem to understand math better than the rest of my classmates, i began to drown out my teachers explaination for the rule. While she was about half way through with explaining mixed decimals i came up with an unsolvable question. Like I said before, I understand how to turn a repeating decimal into a fraction, but how would I turn a repeating .9 into a fraction? We all know it would equal 9/9, but doesn't 9 over 9 also equal 1? Even though it comes very close to one, it never really equals one. I'm very confused about this and i would love it if you could clear this up for me.
Answered by Penny Nom.
The 20 kilometer walk 2002-08-20
From A student:
Answered by Penny Nom.
100 from four 9's 2002-03-27
From A student:
My teacher gave us a math problem to try and figure out and I am stumped. The problem was this.... by only using four nines, how can you get an answer of 100? You can add, subtract, multiply or divide...anything you need to do ,but you can only use four nines.
Answered by Leeanne Boehm.
F = -3 + 3 2002-03-19
From Jessica:
F= -3 + 3 WHAT IS F?????
Answered by Penny Nom.
When will the calendar be the same as 2002? 2002-02-20
From John:
When will the calendar be the same as 2002? I know the answer is 2013, but I don't know how to answer this mathematically, or if it is possible to do so. This is a ninth grade level algebra question my daughter received from her teacher. Any ideas?
Answered by Chris Fisher, Patrick Maidorn and Penny Nom.
What is 20 to the thousandth power? 2002-02-12
From Kristi:
What is 20 to the thousandth power?
Answered by Paul Betts.
50% 2002-01-15
From Lakarrieh:
4 is 50% of what number?
Answered by Penny Nom.
450 students 2001-12-19
From Jessie:
My teacher told me that the number of ways of lining up the 450 students in our school is larger than the number of atoms in the universe. Is this right?

This question came to Good Question, a regular feature on the CBC Morning Edition radio show in Saskatchewan.

Answered by Denis Hanson and Harley Weston.
Negative numbers 2001-11-15
From Jewel:
If zero means nothing or an empty set, then how can a number be less than zero, as in negative number? My understanding of negative numbers is distance from a set point in a given direction. Thus having a negative and positive side of a line is arbritary and is related to displacement rather than value. Am I in error?
Answered by Penny Nom.
Column doesn't add up to 100% 2001-10-17
From A student:
why don't some tables I'm studying in a column add up to 100%? Example: N=338, but responses to questions asked in survey I'm studying equal of 24.3, 9.8, 43.8, DON'T add up to 100%. I'm assuming that some people surveyed out of the 338 didn't bother responding, but is there another problem related to proportion or ratio being used, but improperly labeled on graph?. Note at bottom of table says: "number in parenthesis are numbers of cases" and 338 was in parentheses. I'm lost.
Answered by Penny Nom.
60 seconds in a minute 2001-10-11
From Andy:
I am a fourth grade teacher. Yesterday my students asked "Why are there 60 seconds in a minute?" Which also led to 60 minutes in an hour? I have had trouble determining why the number 60? Any help would be appreciated.
Answered by Penny Nom.
Zero as an exponent 2001-10-04
From Wendy:
How do I explain to kids that i.e. 5 exponent 0 = 1?

Does 0 exponent 0 = 1?

Answered by Leeanne Boehm and Penny Nom.
The 100 chart 2001-09-28
From Nich:
Am I suppose to use the 100 chart for these questions.

Question One:
I am a 2 digit number my tens digit is 2 more than my one digit my 1 digit is between 4 & 6. What # am I ?

Question Two:
I am a 2 digit # I am greater than 40 but less than 60 my tens and ones digits are the same I am a odd number what am I ?

Answered by Penny Nom.
0.999999=1? 2001-09-06
From Catherine:
Hi! My teacher told us that 0.9 repeating equals one. We discussed how this is true. But, I was wondering if there is a proof that this is true. If so what is this called? I was trying to find information, but, it's hard when you don't know the name.
Answered by Walter Whiteley.
Repeating decimals 2001-04-21
From Sarah:
Hi, I'm working on a project for school. The theory I choose was "When turned into a fraction, a repeating decimal has a denometor that is a multiple of three." I have a couple of questions about this topic. My first question is, have you ever heard of this, and what can you tell me about it? My second question is, when I was testing this theory I came across .999... now, when this is a fraction it is 9/9 which is equal to one. The denometor is a multiple of 3, but it's a whole number. I don't understand how a decimal can be equal to a whole number since a decimal is a piece of a whole number. Please don't just show me a math problem, I don't want to see a math problem. I want to see an explanation of this theory and the decimal .999...
Answered by Penny Nom.
1 = 0.999... 2001-04-13
From Joan:
I have a middle grade math question for you. I would like to know why .9999... = 1 ? I can not use algebra to show this or the following: We agree that 2 = 2 and that 2-2 = 0, so

0.000... = 0 therefore 0.9 = 1
----------OR--------------- 1/3 = 0.333333 and 3 X 1/3 = 1, so if 3 X 0.333... = 0.999... then 0.999... = 1

My teacher says that I can not use the above example to show why this is true, and that I must use a couple different examples. He says that there are several other ways. Do you know any? I could really use the help because I can't think of any other ways to show this is true. Thanks for any help you can give.

Answered by Penny Nom.
4160 2001-03-07
From Jessica:
The product of two consecutive page numbers in this book is 4160. What are the page numbers?
Answered by Penny Nom.
Why is 0! = 1? 2001-01-30
From Diane:
Every math book always claims that 1!=1 and 0!=1 are givens, and that we should just memorize it. i understand the 1! part, but where is the basis for claiming that 0!=1????
Answered by Walter Whiteley.
1234567890 2000-09-14
From Bradley Kloetzly:
Can you find two whole numbers, with the smallest possible difference between them, which when multipled together equal: 1234567890?
Answered by Harley Weston.
10,000! 2000-07-21
From Lauren:
Hi I was just wondering if you could tell me how many zeros are in 100,000! (factorial.)
Answered by Denis Hanson.
A 100-gon 2000-05-24
From Chris Mohr:
What is a 100-gon called?
Answered by Harley Weston.
The side length ratios of some triangles 2000-04-04
From Alexis Lockwood:
I am doing a project for my Math 30B class regarding the side length ratios of 45-45-90 degree and 30-60-90 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter.
Answered by Harley Weston.
1000 percent 2000-03-17
From Matt Stevenson:
If one invests $4000.00 and makes 1000% on the investment would he/she have $40,000.00?
Could one figure this by: $4000.00 * 10.0 = $40,000.00?
So is 10 times a number the same as 1000%?

Would 100 times a number be the same as 10,000%?

Answered by Penny Nom.
More on googols 2000-02-23
From Kevin Brennan:
Could you please give me a couple of examples of when you MATH guys would use a google. Do youu measure, like, galaxies with it ? Or was it created to keep track of Mr Gate's bank account.
Answered by Penny Nom.
.400 in Baseball 1999-12-15
From Nieve Nielson:
I have several questions to ask about the probability of getting a .400 in baseball:
  1. What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?

  2. What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind:

  3. Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?

Answered by Chris Fisher.
Bases other than 10 1999-12-06
From Garret Magin:
We are doing a lesson on numbers of other bases than 10. We are working with binary, octal, and Hexadecimal. I was wondering what is used to represent number of different bases other then 16? Does it just continue on with the alphabet and if so what happens when you get to Z. It would be a help if you could answer this because it is really bugging me. And none of the math teachers at my school could let me know.
Answered by Claude Tardif and Patrick Maidorn.
Powers of zero 1999-10-31
From Salina Young:
Hello! I have two questions to ask about the power of "0".

First, what is the value of "0' to the power of "0"? And why?

Second, what is the value of "0" to the power of "2" or '3" etc? And why?

Thank you for your help.
Answered by Walter Whiteley and Harley Weston.

A googol 1999-10-06
From Kevin Brennan:
describe to me a guegoll is that how u spell it?

it sounds like that
Answered by Penny Nom.

Y2K? 1999-09-03
From Mike Putzakulish:
In Y2K, the "K" stands for thousand, but where did the "K" come from? I know it's not a Roman Numeral, but what is it??
Answered by Chris Fisher and Harley Weston.
Division by zero 1999-09-02
From Joshua B. Mariano:
Why can't I divide a number by zero. When I put in my calculater 0 divided by 7 it equals 0. But when I put 7 divided by zero my calculater say's error. Why can't this be solved? What is the answer? Is there a paper on it? Help?
Answered by Walter Whiteley.
Repeating decimals 1999-05-21
From Stan:
Hi, I am in Honors Math, and have confronted everyone, including teachers, about repeating decimals. What interests me is the number 0.9... and 1. Everyone says that since there is no number between 0.9...(repeating) and 1, that 0.9... = 1. However, isn't a repeating number a representation of a number, and not a real number? Let's look at it this way. 0.9 is close to 1. 0.99 is closer. 0.99999999999999 is even closer. so, 0.9... is a representation of it's closeness to 1. it's an active number... I don't understand how 0.9... is equal to 1. Please help me prove that 0.9... does NOT = 1.
Answered by Penny Nom.
Base 2 to Base 10, conversion, convert 1999-05-08
From Larry Bader:
101000112 is the same as what number in Base ten?

a. 83
b. 128
c. 93
d. 326
e. 163
Answered by Penny Nom.

Large Numbers 1999-04-05
From CK:
Hello. I need a lesson plan for grades 4 to 7 dealing with the concept of large numbers. Specifically, how to teach scientific notation. The lesson plan has to deal with the following: the size of the universe is so huge that is is almost beyond the ability of the mind to comprehend. One way is to measure...
Answered by Chris Fisher.
Finding Excluded Values 1999-04-01
From Lorraine Le Cam:
The question asks me to find the value of the variable that must be excluded in each rational expressionion. The operation is:

a - 2

How do I work this out?
Answered by Harley Weston.

Place Value 1999-01-05
From Reg:
I work in a Section 27 classroom with various grades. I am looking for assistance on how to deliver a lesson on place value:decimal numbers keeping in mind that they need to see it (visual) to comprehend. I am looking for grade 4-6 level.
Answered by Jack LeSage.
Indeterminate forms 1998-12-11
From R. Dixon:
What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity.
Answered by Walter Whiteley and Harley Weston.
The sum of the angles of a triangle is 180 degrees 1998-02-19
From Quin Liu:
How do you prove that the sum of the angles of a triangle is 180 degrees? Is there a proof? what is it?
Answered by Chris Fisher.
0! 1997-03-02
From Donna D. Hall:
I am looking for a quick and easy explanation as to why 0! is 1.
Answered by Walter Whiteley and Denis Hanson.
Why is a circle divided into 360 degrees? 1996-09-30
From Kurtis Kredo:
I was recently wondering why a circle has been divided in to 360 degrees. When I asked my physics teacher he could not think of an answer. His guess is that it probably has to do with people long ago using the base 6 number system. I have a small inkling that it has to do with easy conversion or usage with radians or grads.
Answered by Chris Fisher.
a to the power zero 1996-06-03
From Beti:
Why is a number to the power 0 equal to 1?
Answered by Harley Weston.
800 poules pondent 800 oeufs en 8 jours 2007-12-17
Answered by Claude Tardif.
un jardinier plantent 10 arbres 2007-09-30
From yannick:
un jardinier plantent 10 arbres.il a reussi a les disposer en formant 5 ligne de 4 arbres. retrouver une disposition possible
Answered by Claude Tardif.
exposant 0 2007-01-25
From Judith:
Je suis stagiaire dans une classe de sixième année et j'aimerais pouvoir expliquer à mes élèves pourquoi tous les nombres exposant 0 donne 1 comme réponse. ( 10 exposant zéro = 1) Merci!
Answered by Claude Tardif.
Un polyedre ayant comme face 20 triangles 2000-08-02
From Sonia:
J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux.
Answered by Chris Fisher.
Exposant à la 0 2000-07-04
From Sylvie:
J'aimerais savoir combien fait 0 exposant 0.
Answered by Claude Tardif.



Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.



Home Resource Room Home Resource Room Quandaries and Queries Mathematics with a Human Face About Math Central Problem of the Month Math Beyond School Outreach Activities Teacher's Bulletin Board Canadian Mathematical Society University of Regina PIMS