Question

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

`21/50`

Answer 1

Given: `21/50`

Step-wise calculation:

1. Write the fraction `21/50`.

2. Note that the denominator 50 can be factorised into prime factors as 50 = 2 × 5².

3. Since the denominator only contains prime factors 2 and/or 5, the decimal expansion of the fraction will be terminating.

4. To find the decimal, divide numerator by denominator: `21/50 = 0.42`

The decimal expansion of `21/50` is 0.42.

This decimal expansion is terminating because its denominator has only the prime factors 2 and 5.

Hence, `21/50 = 0.42` terminating decimal expansion.