







The decimal form of a fraction 
20180112 

From Tom: Prove that the decimal representation of the quotient of 2 integers must repeat (if it does not terminate). Answered by Penny Nom. 





Changing a mixed number to a decimal 
20170923 

From karla: to change an improper fraction into a decimal 5 3/4 equals Answered by Penny Nom. 





Long division with decimals 
20170616 

From Kenneth: Hello:
Why is it recommended to move the decimal from a divisor when dividing so that the divisor is a whole number?
I know how to divide by moving the decimal from the divisor, but I cannot explain the reason.
I thank you for your reply. Answered by Penny Nom. 





Is 22/7 bigger or smaller than 3.14? 
20151106 

From Natalie: Is 22/7 bigger or smaller than 3.14? Answered by Harley Weston. 





The sum of two repeating decimals 
20151022 

From Kaitlin: Here is the question I am struggling with:
Is the sum of two repeating decimals always repeating decimal? Explain your answer and give an example.
I answered this question thinking that no you cannot but only when adding 0.9 repeating, but my professor said this was incorrect.
Thanks for the help!
Kaitlin Answered by Penny Nom. 





Repeated decimals 
20150509 

From Vir: Years ago I (re?)discovered 'cyclic division'. For example: if you arrange the number along a circle and put the number 142857 at the centre
all the numbers taken cyclically, starting with 1, are fully divisible by 37. Whatever the starting point of this number, it remains fully divisible by 37.
what is more, the number can be formed by taking the digits clockwise as well as anticlockwise..This I call "full cyclic divisibility". In many cases, only clockwise cyclic divisibility is possible. But I have not come across a case where ONLY anticlockwise divisibility occurs. Thus clockwise cyclic divisibility seems to be favoured. Could this be construed as a sign of chirality in mathematics?.. Answered by Chris Fisher. 





How do I make fractions into decimals? 
20140531 

From jay: Hi,
I wanted to know how do I make fractions into decimals example 1 3/8? Answered by Penny Nom. 





8 3/4 as a decimal 
20130515 

From Luisa: How to make 8 3/4 into a decimal Answered by Penny Nom. 





3.8 x 2.2 
20110818 

From Isaac: Question from isaac, a student: I am struggling in math & I need help on multiplying 3.8 x 2.2. Can you helpme Answered by Melanie Tyrer and Harley Weston. 





Write 3 1/5 in decimal form 
20110324 

From Stephenie: converting fractions????
3 1/5 into decimal??? Answered by Penny Nom. 





How are decimals used in every day life? 
20100901 

From Keith: how are deciminal used in every day life Answered by Tyler Wood. 





Does 1= 0.9999....? 
20100407 

From Asia: Does 1= 0.9999....? There seems to be different opinions on this. Answered by Robert Dawson. 





Decimals and fractions 
20100316 

From fay: why do we use decimals in place of fractions in everyday life? Answered by Robert Dawson. 





Working with decimals 
20100129 

From linda: Write 3 numbers that are between the following:
2.15 meters and
2.17 meters Answered by Harley Weston. 





Ordering numbers 
20090919 

From tattiana: how do you order these numbers from greatest to least .625,.75,.20, and .5 Answered by Penny Nom. 





Integers and decimals in day to day life 
20090629 

From mitichie: can you tell use of integers and decimals in our day to day life. Answered by Penny Nom. 





How many eighths are there in 1.25? 
20090506 

From Tamara: How many eighths are there in 1.25? Answered by Penny Nom. 





More on mills 
20090325 

From Kenneth: If I want to express 13 mills as a decimal part of $1.00, the answer
is $0.013. This amount is found by dividing 13 mills by 1000
mills/$1.00.
Can 13 mills be expressed as a decimal part of another amount instead
of $1.00? For example, express 13 mills as a decimal part of $1.50
or express 13 mills as a decimal part of $0.10. What would these
amounts be? Answered by Robert Dawson. 





mutiplying decimals 
20090224 

From telly: how to do this sum0.24*0.398 Answered by Robert Dawson and Penny Nom. 





Decimals and fractions used in our daily lives 
20081204 

From josh: i have a projecct due friday and i need to know, how are decimals and
fractions used in our daily lives. i am having trouble coming up with
ideas. i need seven more that dont involve money or recipes. please
help me. Answered by Harley Weston. 





How do I compare fractions and decimals? 
20081118 

From Alexis: How do I compare fractions and decimals ? Answered by Penny Nom. 





A ratio to a decimal 
20081114 

From manny: Express 22 : 5 as a decimal. Round to the nearest hundredth Answered by Penny Nom. 





What are the equivalent to 0.68? 
20081028 

From clay: what are the equivalent to 0.68 ? Answered by Penny Nom. 





0.99999.... 
20080923 

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. 





0.151515...=15/99 
20080908 

From Emma: This week, my Algebra teacher told us about the pattern between infinitely repeating
decimals and their corresponding fractions.
(ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.)
I was just wondering the reason why this pattern occurs.
Is there a certain element that causes this pattern to occur?
Thanks
Emma Answered by Penny Nom. 





Nonterminating, nonrepeating decimals 
20080803 

From Peter: How do you take a random, nonterminating, nonrepeating decimal into a fraction? Answered by Stephen La Rocque. 





.9 repeating plus .2 repeating 
20080610 

From megan: How do you express the addition of .9 repeating plus .2 repeating? Answered by Penny Nom. 





How do you add decimals? 
20080605 

From nyheashiacurry: how do you add up decimals? Answered by Janice Cotcher. 





Repeating decimals 
20080310 

From Blaine: Is it possible to put a repeating decimal number into a calculator to solve a problem?
EX: Write 39.3939... as a fraction. Answered by Penny Nom. 





Repeating decimals 
20080129 

From Malise: Write each repeating decimal using bar notation.
0.428571428... Answered by Penny Nom. 





How many bags of cement will I need? 
20080115 

From James: I want to extend my front porshe more to the left atleast 14' 1" length wise and 5' 1" width wise with 4" thickness. Now i already decimalized in feet those inches, resulting with 14.08 length and 5.08width and 0.33 of thickness. I then Get my square feet of 71.53. And go on to cubic feet getting a 23.60 in cubic feet. Now i want to convert to cubic yards so i then divide 23.60 into 27 and get 0.87. Now my question is how would i use this to go and buy the necessary bags of cement knowing that a 94 lb. bag of cement is 1 cubic foot of bulk material. To fill 4 inch of thickness and 14' of length and 5 of width? Answered by Stephen La Rocque. 





Repeating decimals 
20071202 

From Jack: I've been working on an equation to support my theory of repeating decimals. Specifically the correlation between the 9 and 11 denominators. I wanted to know if there was already an equation to describe this correlation? Mine is x/11=.b repeating and b=9x, so if you use any single digit number for x (say 4) if 9 x 4 = 36 then 4/11 = .36363636... I just want to know if this theory already exists and if so, what is it called? Answered by Victoria West. 





A decimal to a fraction 
20071101 

From Lisa: i am trying to turn a decimal into a fraction. my example is to turn 10.5 into a fraction at its lowest form Answered by Penny Nom. 





0.24 1/2 
20070906 

From Kenneth: The fraction, 1/2, in 0.24 1/2 occupies the 1/100 place along with the 4.
If the fraction, 1/2, is changed to a decimal, as in 0.245, the last 5 in 0.245 occupies the 1/1000 place.
Why doesn't the 1/2 in the decimal 0.24 1/2 occupy the 1/1000 place (0.001) instead of the 1/100 place? Answered by Stephen La Rocque. 





Equivalent fractions 
20070831 

From Darlene: What is the equivalent decimal for 0.3 and 6.53 Answered by Penny Nom. 





Division by decimals 
20070815 

From Brooklyn: I am studying for an exam, and I will not be able to use a calculator. I can not figure out how to do division is the number on the outside of the box is a decimal. Ex: 2/6.3=X Can you please help me figure this out? Answered by Penny Nom. 





Repeating decimals and rational numbers 
20070531 

From lil: Why are repeating decimals considered rational numbers? Answered by Penny Nom and Gabriel Potter. 





Fractions, decimals and profit 
20070529 

From fatima: how can i change a fraction into a decimal and how do i change a
decimal into a fraction................
anther question please what does making a profit have
to do with percentage change!!!!!! Answered by Penny Nom. 





A 15% tip 
20061206 

From Danielle: When she eats at a restaurant,Viviana like to leave a 15% tip,multiplying the price of the meal by 0.15. Franklin usually leaves a 20% tip,multiplying the price by 0.20.They both round up to the nearest $0.05. How much tip would Viviana leave for a $24.85 meal? Answered by Penny Nom. 





Converting fractions to decimals 
20060725 

From Diane: HOW DO I CONVERT A FRACTION TO A DECIMAL? (E.G,. 8/14 to ? )
And HOW DO I DIVIDE A FRACTION (e.g., 1/14 divided by 3) and then convert that answer to a decimal? Answered by Penny Nom. 





Common fractions to decimals 
20051125 

From A student: how do u turn 8 over23 into a decimal and how do u turn 8 over 29 into a decimal Answered by Penny Nom. 





Equivalent fractions 
20050913 

From Cindy:
I am a parent and aunt of a 5th grader.
My nephew has asked me what the equivalent decimal is of 0.4. Does he change it to a fraction or just add a zero either before or after?
Answered by Chris Fisher and Harley Weston. 





0.810 and 0.801 
20031024 

From Ahmed:
could you please tell me what is the greatest decimal fraction formed of the digits 0, 1 , 8? Is it 0.810 or 0.801, please give me the reason of the answer in details and the references if it possible. Answered by Penny Nom. 





Why percentage? 
20030903 

From Vicky: My cousin aske me a question about the use of percentages and I'm not sure how to answer it. He wants to know why when there is a sale in a shop we use percentages and not fractions or decimals. Answered by Penny Nom. 





Repeating decimals 
20030108 

From A student: If k=.9repeating, and 10k=9.9repeating then 10kk=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify? Answered by Penny Nom. 





Decimals in everyday life 
20021124 

From Fritz: How do you use decimals in your every day life? Answered by Penny Nom. 





0.99999... 
20020926 

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 number of decimal places in 1 over a power of 2 
20020912 

From Allan: Does anyone notice that the maximum number of decimal place of the number 2 dividing 1 and its increment (4, 8, 16...etc) is the same as the power of number 2? eg. 2^{2}=4, thus the max number of decimal of ^{1}/_{4}=0.25 which is 2 decimal place and 2 is the number of power of 2 take 64 as example: 2^{6}=64, and take ^{1}/_{64}=0.015625 which has 6 decimal place (and is the power 6) Is there such a law in math? If yes, can you tell me what it is? Or is this my discovery? Answered by Paul Betts. 





Common fractions to decimal fractions 
20020402 

From Natalie: My questions are: "how can I change 23/60 into a decimal. and give my answer to 2dp."?????????? 2nd question:for each of these pairs, which is bigger?
4/7 or 36%____________ 3/11or 0.29____________ 14/24 or 0.57___________ Answered by Penny Nom. 





Multiplying decimals 
20020310 

From Kaitlin: I just recently had a test on multiplying decimals and I did not do really well on it. Only 5 kids out of 19 got a passing grade. My teacher says that she will give us a different test and we can take it again, but I'm still not sure of it. My teacher has taught me a lot and she had done a wonderful job of it but I'm just confused with where to put the decimals and stuff like that. I have a math practice workbook that I do for fun and they have nothing on decimals in it. I have checked on websites to try to find worksheets but I really couldn't find a good one. Can you please help me either give me some tips or clues or send me a worksheet. Answered by Penny Nom. 





Fractions in lowest terms 
20011205 

From Thomas: how to change decimal to a fraction in the lowest terms .7 .65 .019 .0111 .225 .1225 .625 .25 .025 .26 .875 .5 .75 .750 .33 .09 .44 .15 .12 .90 .044 .2500 .95 .500 .02 .40 .125 .1276 .00009 .45 .125 .1276 .375 .975 .054 .0005 .20 .2 .0001 .85 .80 .9 .0007 9.8 10.17 25.75 48.4 80.35 19.64 276.20 31.042 18.1034 Answered by Penny Nom. 





Commas in numbers 
20010906 

From Mike: When did the Ontario Education system drop the use of commas in large numbers and replace with a space? Why? Answered by Walter Whiteley. 





Repeating decimals 
20010421 

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... 
20010413 

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 22 = 0, so
1.00000...... 0.99999.....  0.000000...... and 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. 





Finite nonperiodical numbers 
20010327 

From Wouter: Is there anyone who knows the official name for decimal finite nonperiodical numbers such as 0.4 or 0.25 as opposite of numbers like 0.3333333... or 0.28571428571428...? Answered by Penny Nom. 





The repetend in repeating decimals 
20010321 

From Sharon: What is the name for the bar over the repetend in repeating decimals? Also, what is the name of the long division "house"? Answered by Penny Nom. 





More repeating decimals 
20010117 

From Alan: I am neither a math teacher nor a student, but I hope you will consider my question anyway. I recently was discussing repeated decimals with a friend, and went on the web to find out more about a pattern was looking for years ago. In doing so I came upon your correspondence on repeating decimals. . . . Answered by Chris Fisher and Penny Nom. 





Multiplication of fractions 
20010108 

From Angela: Questions:
1. represent multiplication of fractions via an area model 2. describe why, not just how, to round decimals Answered by Penny Nom. 





Mixed Fractions 
20001209 

From Tim Finch: My son is having problems with mixed decimals and mixed fractions.. I am unable to find any information or examples on this subject so I can show him how to do it.. for example how do you make a mixed decimal or fraction out of 7/16 Answered by Penny Nom. 





Dividing with decimals 
20001115 

From Alex: I teach math and my class and I were discussing the dividing of decimals. I explained that if there is a decimal in the divisor, it needs to be moved and so does the decimal in the dividend. My question is why is it necessary to move the decimal point in the divisor before dividing? Answered by Penny Nom. 





Multiplying decimals 
20001016 

From Lily: I need help with mutiplying decimals (example) 2.28*0.48( * = times). Answered by Harley Weston. 





Repeating decimals 
20001006 

From Mary O'Sullivan: I understand that with repeating decimals (those with a pattern), the number of digits repeated is put into fraction form with the same number of 9's ex. 0.4444 = 4/9 0.145145145 = 145/999 How can I explain why this is so? Some inquisitive 8th graders are anxious to find out! Answered by Penny Nom and Walter Whiteley. 





Rational Numbers 
20000914 

From Josh Kuhar: How can you tell a number is rational? Answered by Harley Weston. 





Rounding 
20000415 

From Tawana Brown: I was uncertain as to whether a number such as 85.25 rounding to the nearest tenth would be 85.3 or 85.2. I thought I had heard somewhere that if 5 is the last number that you don't round up. But I have also heard that anything 5 and above you do round up. It's been awhile since I've done rounding, so I need a refresher course. Answered by Walter Whiteley and Harley Weston. 





The sum of repeating decimals 
20000215 

From Caitlin Harris: Express 0.111... + 0.121212... + 0.123123123... as a repeating decimal and its equivalent fraction. Show work. Also, are there any extensions to this problem? In other words, are there any questions that we could ask that may be related to this problem? Answered by Penny Nom. 





Repeating decimals 
19991122 

From Andrew: Is 1.9 repeating the same as 2? Answered by Walter Whiteley. 





Fractions, percents and decimals 
19990919 

From Sue Farr: My son is in 5th grade, and I can't seem to find any papers that have a simple explanation of how to convert decimals into fractions, percents into decimals, and viceversa. Answered by Harley Weston. 





Repeating decimals 
19990918 

From Kavoos Bybordi: I dont know how to change a reccuring decimal to a fraction please could you tell me the method. Answered by Penny Nom. 





Repeating decimals 
19990521 

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. 





The square root of two is never supposed to end 
19990306 

From a wondering student: i am algebra II and am in the 9th grade. today we were talking about rational and irrational numbers. When we were talking about square roots my friend and i were talking and we thought of something. if you have a square with sides of length one then the diagonal of the square is the square root of 2. Now the square root of two is never supposed to end. But the diagonal of the square ends so therefore doesn't the square root of 2 end. our math teacher did not really answer our question because it was not in the lesson plan and not to many people would see where we were coming from. the answer is really bugging me and i would like to have your input. Answered by Jack LeSage and Penny Nom. 





Dividing Decimals 
19990206 

From Melanie Campbell: i ugently need to know how to divide a decimal by a decimal eg:6.0 divided by 2.4 i need to show all working on a basic skills exam please help!!!! mel Answered by Jack LeSage. 





Turning Fractions into Decimals 
19990116 

From Lynn: How do you do it step by step Answered by Jack LeSage. 





Place Value 
19990105 

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 46 level. Answered by Jack LeSage. 





6.99999... = ? 
19981205 

From Tom: I have had a rather heated arguement with my students. Please settle this for me. Solve <,>, = 6.99999... __ 7 Thank you. Answered by Penny Nom. 





Terminating decimals 
19981116 

From Debra Karr: A college student studying elementary education asked me a question that I could not think of the correct answer. How can you look at a fraction and tell if is a terminating or non terminating decimal? Answered by Jack LeSage and Penny Nom. 





Fractions 
19981027 

From Jessica Braimoh: I have a problem that I just can't figure out!! Put into a fraction a) 1.157... b) 0.046... c) 0.032... d) 0.3234... Please show how you got the answer and how you came to it(step by step) Thanks Jessica Braimoh grade 9 Ontario Answered by Harley Weston. 





Repeating Decimals 
19981001 

From Chris Norton: Could you PLEASE give the formula to find out the number of digits in a repeating decimal before it repeats. I have been trying to get it for weeks from Math sites on the Internet. Can you please, please help me ? Chris Norton Answered by Chris Fisher and Penny Nom. 





Rational and Irrational Numbers 
19980919 

From Ri: I am trying to explain rational & irrational numbers to my niece who is grade 7 and am having difficulties. Could you please explain the difference between rational & irrational numbers. Thank you Ri Answered by Penny Nom. 





Repeating Decimals 
19970124 

From Grant Reed: Is there a way to tell that the repeating decimal for 1/17 has no more than 16 repeating digits? Answered by Penny Nom. 





Repeating decimals 
19960909 

From Alice: What is the line called that is placed over the decimal to show that it is infinitely repeating? Answered by The Centralizer. 

