Question

A rational no. Can be express as a terminating decimal if denominator has which factors?
Argent

Answer 1

Hey there!!

Any rational number can expressed as a terminating decimal if it is in the form of 2ˣ·5ⁿ

x and n are POSITIVE

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

If the denominator is in the form of $\bold{</strong><strong>{2}^{m} \times {5}^{n} </strong><strong> }$

Or,the denominator is the factor of 2 and 5 both.

$\mathfrak{\large{\underline{\underline{</strong><strong>E</strong><strong>x</strong><strong>p</strong><strong>l</strong><strong>a</strong><strong>n</strong><strong>a</strong><strong>t</strong><strong>i</strong><strong>o</strong><strong>n</strong><strong>:-}}}}$

Let X = $\bold{</strong><strong>\frac{p}{q} </strong><strong>}$be a rational number,such that prime factorisation of q is of the form $\bold{</strong><strong>{2}^{m} \times {5}^{n} </strong><strong> }$ ,where m and n are non - negative integers.

Then the decimal expansion of X will be terminate.