GMATD11 wrote:

Question:: Convert X=.262626.... into a fraction.

Answer ::

100x=26.2626....

100x-x=26

99x=26

x=26/99

Why x is subtracted from 100x?

To get rid of the infinite chain of 26s

x = .26262626....

100x = 26.26262626....

The right sides of the equations are the same. When we subtract, we get rid of .26262626.... and that is what we want if we want to convert a non terminating repeating decimal to a fraction. Else with infinite .26s, how many zeroes will you put in the denominator to convert it to a fraction (i.e. say 2.6 = 26/10, .2626 = 2626/10000, what about .26262626... infinite?)

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