Question

The decimal expansion of 13457/3125 will terminate after how many places?

Answer 1

3125=5×5×5×5×5

=5⁵

The power of 5 determines after how many places the decimal would terminate.

So,13/3125 will terminate after 5 decimal spaces.

HOPE IT HELPS YOU....

Answer 2

The expansion will terminate after the places of decimal depending upon the maximum power of $5$ in the divisor

We can write $3125$ as $5^{5}$

$\frac{13457}{3125}=\frac{13457}{5^{5} }$

So the decimal will terminate after 5 places in the expansion of this expression and the expansion will be $4.30624$

Lets take another example to understand the method

$\frac{627}{25}=25.08$

since $5^{2}$ is here, the expression terminates after two places.

$\frac{627}{125} =5.016$

Since $5^{3}$ is here, the expression goes upto three places after decimal

Learn more about decimal expansions

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