How to write a recurring decimal 0.17(7 is recurring) as fraction ?

To express the recurring decimal 0.17(7) as a fraction, you can use the following steps:

Let x = 0.17(7), where the 7 is recurring.

Multiply x by 100 to move the recurring part two decimal places to the right:
100x = 17.77(7)

Subtract x from 100x to eliminate the recurring part:
100x - x = 17.77(7) - 0.17(7)

This simplifies to:
99x = 17.6

Now, divide both sides by 99 to isolate x:
x = 17.6 / 99

To further simplify the fraction, you can find the greatest common divisor (GCD) of 17.6 and 99, which is 4.

Divide both the numerator and denominator by the GCD (4):
x = (17.6 / 4) / (99 / 4)

Simplify the fraction:
x = 4.4 / 24.75

Finally, divide both the numerator and denominator by their greatest common divisor, which is 0.25:
x = (4.4 / 0.25) / (24.75 / 0.25)

Simplify further:
x = 17.6 / 99

So, the recurring decimal 0.17(7) can be expressed as the fraction 17.6/99.