Question

Express the following recurring decimal in the form of a rational number `bb(("in fraction form" p/q)`:

`0.bar(24)`

Answer 1

To express the recurring decimal `0.bar(24)` as a fraction, let:

x = 0.242424...

Since the repeating block “24” has 2 digits, multiply both sides by 100:

100x = 24.242424...

Now subtract the original equation from this:

100x – x = 24.242424... – 0.242424... 

99x = 24

`x = 24/99`

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor 3:

`x = 8/33`

So, the recurring decimal `0.bar(24)` expressed as a fraction is `8/33`.