Question

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

`1/7`

Answer 1

Given: Rational number `1/7`

Step-wise calculation: Perform long division of 1 by 7

1 ÷ 7 = 0.142857142857...

The quotient starts as 0.

The decimal part is 0.142857, which repeats indefinitely.

Specifically, the block “142857” repeats endlessly.

The decimal expansion of `1/7` is `0.bar(142857)` where 142857 is the repeating pattern.

This is a non-terminating recurring decimal expansion because the digits repeat endlessly in a cycle of length 6.

This is also a classic example of a rational number with a repeating decimal pattern.

Hence, `1/7 = 0.bar(142857)` non-terminating recurring decimal.