SOLUTION: 3.25 as a fraction only 5 repeating

Question 1108967: 3.25 as a fraction only 5 repeating

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe you are asking how to find the fraction of 3.255555555555........, where the 5 repeats endlessly.

i think this is the way to do it.

let x equal your number.

you get x = 3.2555555.......

you want to multiply the number so the the repeating decimals are directly to the left of the decimal point and directly to the right of the decimal point.

to get the repeating decimal directly to the right of the decimal point, multiply both sides of that original equation by 10 to get:

10x = 32.55555.................

to get the repeating decimal directly to the left of the decimal point, multiply both sides of the original equation by 100 to get:

100x = 325.55555......................

now subtract 10x = 32.55555..... from 100x = 325.55555...... to get:

90x = 325 - 32

this results in 90x = 293.

solve for x to get x = 293/90.

that's your fraction.

convert that to a mixed fraction to get 3 and 23/90.

enter 293/90 in your calculator and it will tell you that the number is 3.255555......

enter (3 + 23/90) in your calculator and it will tell you the same.

that tells you that you did the conversion correctly.

here's a reference from the web on how to do it.

https://www.basic-mathematics.com/converting-repeating-decimals-to-fractions.html

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