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| Math Central | Quandaries & Queries |
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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! |
Savanna,
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,
Penny
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