Question

Write the decimal expansion of the following rational number and state which type of decimal expansion has?

`3/11`

Answer 1

Given: `3/11`

Step-wise calculation using long division for decimal expansion:

Divide 3 by 11.

11 goes into 3 zero times, so start with 0.

Add decimal point and bring down 0, now divide 30 by 11.

11 × 2 = 22, remainder 30 – 22 = 8.

Bring down 0, divide 80 by 11.

11 × 7 = 77, remainder 80 – 77 = 3.

Bring down 0, divide 30 by 11.

The pattern repeats from here remainder 3 again.

So the decimal expansion is `0. bar27`

which means the digits “27” repeat indefinitely.

The decimal expansion of `3/11` is `0. bar27`, a non-terminating recurring decimal.