Question

Write the decimal expansion of those numbers from the following that have terminating decimals.

`77/175`

Answer 1

Let’s analyse `77/175`:

1. Prime factorise the denominator:

175 = 25 × 7

175 = 5² × 7

Since there is a factor of 7, the decimal expansion should be non-terminating repeating.

2. Simplify the fraction:

`77/175`

= `(11 xx 7)/(25 xx 7)`

= `11/25`

On canceling 7, the denominator becomes 25 = 5² only, which means the simplified denominator has only 5s as prime factors.

3. The decimal expansion of `11/25` is `11/25 = 0.44` which is terminating.

Hence, `77/175` simplifies to `11/25` and since 25 is 5², the decimal expansion is terminating and equals 0.44.

So `77/175 = 0.44` terminating decimal because the denominator in the fraction's simplest form is 25, which only has 5 as prime factors.