Question

Which of the following rational numbers is expressible as a terminating decimal ?

$\left(a\right)\frac{124}{165}\left(b\right)\frac{131}{30}\left(c\right)\frac{2027}{625}\left(d\right)\frac{1625}{462}$

Answer 1

Answer:
(c) $\frac{2027}{625}$


$\frac{124}{165}$
=
$\frac{124}{5\times 33}$
; we know 5 and 33 are not the factors of 124. It is in its simplest form and it
cannot be expressed as the product of ($2^m\times 5^n$)
for some non-negative integers m, n.
So, it cannot be expressed as a terminating decimal.
$\frac{131}{30}$
=
$\frac{131}{5\times 6}$
; we know 5 and 6 are not the factors of 131. It is in its simplest form and it
cannot be expressed as the product of ($2^m\times 5^n$)
for some non-negative integers m, n.
So, it cannot be expressed as a terminating decimal.
$\frac{2027}{625}$
=
$\frac{2027\times 2^4}{5^4\times 2^4}$
=$\frac{32423}{10000}$

= 3.2432; as it is of the form($2^m\times 5^n$)
, where m, n are non-negative
integers.
So, it is a terminating decimal.
$\frac{1625}{462}$
=
$\frac{1625}{2\times 7\times 33}$
; we know 2, 7 and 33 are not the factors of 1625. It is in its simplest form
and it cannot be expressed as the product of ($2^m\times 5^n$)
for some non-negative integers m, n.
So, it cannot be expressed as a terminating decimal.