Question

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

`15/160`

Answer 1

To determine if `15/160` has a terminating decimal, first simplify the fraction `15/160`:

`15/160`

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

= `3/2^5`

= `3/32`

Since the denominator is a power of 2 only in the form 2^m × 5ⁿ with m = 5, n = 0, `3/32` will have a terminating decimal.

To find the decimal expansion:

`3/32`

= `(3 xx 3125)/(32 xx 3125)`

= `9375/10^5`

= 0.09375

Therefore, the decimal expansion of `15/160` is 0.09375 and it is terminating.