Question

Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.

$\left(i\right)\frac{23}{(2^3\times 5^2)}\left(ii\right)\frac{24}{125}\left(iii\right)\frac{171}{800}\left(iv\right)\frac{15}{1600}\left(v\right)\frac{17}{320}\left(vi\right)\frac{19}{3125}$

Answer 1

i) 0.115

We know either 2 or 5 is not a factor of 23, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

ii)

We know 5 is not a factor of 24, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

(iii)

We know either 2 or 5 is not a factor of 171, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

iv)

We know either 2 or 5 is not a factor of 15, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

v)

We know either 2 or 5 is not a factor of 17, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

vi)

We know either 2 or 5 is not a factor of 19, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating