







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. 





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. 





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. 





.9 repeating plus .2 repeating 
20080610 

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





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. 





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. 





Repeating decimals and rational numbers 
20070531 

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





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

