Save time with this short cut method for converting a repeating decimal to a fraction. It even works on a crazy repeating decimal like,

.706438898889

Transcript

Welcome to MooMooMath where we upload a new Math video everyday. In this video I would like to show a shortcut for converting repeating decimals to a fraction.

First the rules.

First, with the numerator, if you only have repeating numbers like .222 you write the repeating number as your numerator.

If you have a mixed recurring decimal like .16666 subtract

Notice the 1 does not repeat like the 6.

The non-repeating number from the repeating number. Make sure the repeating number has the same number of digits as the repeating number.

The denominator rules for non-repeating numbers, add a 0 ,and a 9 for repeating numbers.

Once you write the fraction you then reduce.

Lets work a couple of examples.

Lets start with .333 which is a repeating digit without any non-repeating numbers.

I will write 3 as the numerator, and nine for the repeating number.

I can reduce this down to 1/3

Another example .666

Write 6 which is the repeating number, you have one repeating number so write a nine.

This will reduce to 2/3

Lets go with .833 which has a non-repeating number.

What we will do is subtract the repeating number 83 minus 8 because that is the non-repeating number.

83-8 equals 75, which becomes your numerator.

We have 1 non-repeating number so I will write a 0 and a 9 for the repeating number. 75/90 reduces to 5/6

How about this example?

.1818 we have a repeating number with two digits so I will write 18 and then for the denominator I will write a 9 for each digit which becomes 99 and 18 over 99 can be reduced to 2/11

Lets work a couple more.

.16 we have a non-repeating number.

I will take the repeating number minus the non-repeating number which is 1 and subtract which equals 15

15 over 0 for the non-repeating number and a 9 for the repeating number which becomes 15 over 90 and you can reduce to 1/6

I took 16 minus 1 which is your non-recurring which equals 15 over 90 which reduces to 1/6

The one exception I have found is this,

Take .4166 and you may write the repeating number as 416 but because you have two non-repeating numbers you need at least two repeating numbers. Instead of writing 416 write 4166. From there is would be 4166 minus 41 equals 4125 and 4125 over two non-repeating and two repeating and I cheated and put this in a fraction reduce, which reduces to 5/12

Let me go through two more just to show how this works.

Take .251818 repeating.

Take the repeating fraction of .2518 minus the non-repeating and you have two non-repeating minus 25 because that is the non-repeating portion.

2518 - 25 equals 2493 and you have two non-repeating so write 00 and two repeating numbers so write 99 and simplify to 277/1100 and if you divide it equals .2518

I will show you a crazy number like .70643889889

The repeating is 889 you can see it repeating twice.

I will first write the repeating decimal 70643889 minus the non-repeating of 70643 and when you subtract you get 70573246 and I will write it again 70573246 and use the same rules for the denominator.

For the non-repeating I add a 0 and I have 1 2 3 4 5 zeros.

1 2 3 4 5 and three repeating numbers and three non-repeating 999 and that is your fraction I will not reduce, but test it out and if you divide the numbers it will equal the repeating fraction. It does work

Hope this helps with converting repeating decimals to a fraction

MooMooMath uploads a new Math video everyday.

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Learn even more about fractions with this fraction playlist that covers the basics of fractions!!

https://www.youtube.com/playlist?list=PLurjkZV1ykGa0cb4iAUs2FZLS-ClkRHmq

Tagged under: repeating decimal,recurring decimal,repeating decimal fraction,changing repeating decimal fraction,numbers,decimals,decimals fraction,shortcut,moomoomath

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