i want it immediately

i want it immediately

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This requires some algebra to perform.

You want to define the repeating decimal that you are calculating as x.

In this case, x = 0.137373737...

Now you multiply that times a power of 10 in order to move the decimal place to the right of the last repeating number in the deicmal.

In this case,

137.37373737... so it would be 1000x since you had to move the decimal 3 places to the right.

now multiply by a power of ten to just before the first digit of the repeating part of the decimal.

1.3737.... This would be 10 since 0.137373... * 10 = 1.373737... so 10x

Now you use algebra and get

1000x - 10x = 137.3737... - 1.3737...

The effect is to remove the repeating part from the equation to yield:

990x = 137 - 1 = 136

The fraction is then x = 136/990

this factors down to 68/495

now remember that you have to add one times the denominator (495) to the numerator and you end up with:

563/495

Since there are two digit repeating, you can solve it in the following way:

x = 1.1373737... (1)

100x = 113.73737...(2) multiply by 100 for two digit repeating

(2)-(1): 99x = 112.6

x = 1126/990 = 563/495 <==Answer

## Comments

thanks for the answer