Question

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

`11/4000`

Answer 1

The number `11/4000` has a terminating decimal expansion because its denominator can be expressed as powers of 2 and 5 only since 4000 = 2⁵ × 5³.

To find the decimal expansion, we do the following:

`11/4000`

= `11/(2^5 xx 5^3)`

= `(11 xx 5^2)/(2^5 xx 5^5)`

= `(11 xx 25)/10^5`

= `275/100000`

= 0.00275

So, the decimal expansion of `11/4000` is 0.00275.

Thus, the decimal expansion of the number from the given list that has a terminating decimal is 0.00275.

This is based on the property that a fraction `p/q` has a terminating decimal if the denominator q, in its simplest form, has only 2 and/or 5 as prime factors, which is true for 4000 here.