Question

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

`11.bar(53)`

Answer 1

To express `11.bar(53)` which means the digits “53” repeat indefinitely after the decimal point as a fraction, we do the following:

Let x = 11.535353...

Since two digits repeat, multiply both sides by 100:

100x = 1153.535353...

Now subtract the original x from this:

100x – x = 1153.535353... – 11.535353...

This gives 99x = 1142

So, `x = 1142/99`

This fraction represents `11.bar(53)` as a rational number.

Thus, the answer is `1142/99`.