Question

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$\frac{13}{3125}$

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is C $5$

The given value is $\frac{13}{3125}$ the denominator is 3125 which can be written as:

$3125=2^0\times 5^5$ it is in the form of $2^m\times 5^n$

$max(m,n)=5$

$\therefore$ the expansion is terminating decimal it terminates after

$max(m,n)=5$ places from the decimal [since $m=0,n=5$]