Math CentralQuandaries & Queries


Question from Savanna, a student:

How would put .12 with 2 repeating in fraction? and if you do figure it out (which im sure u will) could you please explain why so i can know how to do it in my future assignments!!!

Thanks a ton!


I am going to convert 0.13777... into a fraction and you can use the same technique for your problem.

Let d = 0.13777... and then perform the subtraction

10d = 1.37777...
-  d = 0.13777...
  9d = 1.24

Multiply both sides by 100 to eliminate the decimal point

900d = 124

and hence

d = 124/900 = 31/225

You can check this by having your calculator find 31/225.

I multiplied both sides of d = 0.13777. by 101 = 10 because the repeat is 1 digit long. If the repeating fraction were 0.13757575... so that the repeat (75) is two digits long I would let d = 0.13757575... and multiply both sides by 102 = 100 before subtracting. Try it and use your calculator to check your answer.

If the repeat were 3 digits long I would multiply by 103 = 1000 and so on.

I hope this helps,

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