Question

Which of the following fractions have terminating decimal expansion?
$\dfrac{1}{{16}}$, $\dfrac{4}{{25}}$, $\dfrac{{22}}{{625}}$, $\dfrac{1}{{1080}}$.

Answer 1

Hint: Before attempting this question, one must have prior knowledge of terminating decimal expansion according to which when a fractional number is simplified into decimal number and the number have finite digits after the decimal have terminating decimal expansion, using this information will help you to approach towards the solution

Complete step-by-step answer:
To check whether the given fractions have terminating decimal expansion or not let’s simplify them
So as we know that a fractional number which have terminating decimal expansion when simplified to decimal number have finite digits after decimal
To choose the terminating decimal expansion fractional number let’s simplify the given fractional number into decimal numbers
Decimal expansion of fractional number $\dfrac{1}{{16}}$ is given by
$\dfrac{1}{{16}} = 0.0625$
Since the decimal expansion of $\dfrac{1}{{16}}$ is 0.0625 which have finite digits after decimal
Therefore the fractional number $\dfrac{1}{{16}}$ have terminating decimal expansion
Decimal expansion for fractional number $\dfrac{4}{{25}}$is given by
$\dfrac{4}{{25}} = 0.26$
So the decimal expansion of fractional number $\dfrac{4}{{25}}$ is 0.26 which consist of finite digits after the decimal point
Therefore fractional number $\dfrac{4}{{25}}$ have terminating decimal expansion
Decimal expansion for fractional number $\dfrac{{22}}{{625}}$is given by
$\dfrac{{22}}{{625}} = 0.0352$
Since the decimal expansion of fractional number $\dfrac{{22}}{{625}}$ is 0.0352 which have finite number after the decimal point
Therefore fractional number $\dfrac{{22}}{{625}}$ have terminating decimal expansion
Decimal expansion of fractional number $\dfrac{1}{{1080}}$ is given by
$\dfrac{1}{{1080}} = 0.000925925....$
For factional number $\dfrac{1}{{1080}}$ whose decimal expansion i.e. 0.000925925… have infinite digits (925) after the decimal point
Therefore fractional number $\dfrac{1}{{1080}}$ doesn’t have terminating decimal expansion
Hence, factional numbers$\dfrac{1}{{16}}$, $\dfrac{4}{{25}}$ and $\dfrac{{22}}{{625}}$ have terminating decimal expansion.

Note: As we know that we solved the decimal expansions of fractional numbers but do you know how we identified that the given numbers are fractional numbers. So fractional numbers can be explained as a representation of part of some whole body or object, its general representation is given by $\dfrac{p}{q}$. Here p represents the numerator and q represents the denominator.