Question

without actually performing long division, state whether the following numbers has a terminating decimal expansion or non-terminating recurring decimal expansion 543/225

Answer 1

Heya !!!!......


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==> We know if any terminating decimal number represent in fraction than it's denominator will be in form of 2m× 5n .
And

Decimal digits of any number depends on value of m and n , If

●We get

m  > n than we get " m " number of decimal digits .
And
If

●We get
n  > m than we get " n "  number of decimal digits . 

So,

$\frac{543}{225} = \frac{181}{75} = \frac{181}{3 \times 5 \times 5} = \frac{181}{ {3}^{1} \times {5}^{2} }$


☆☆Here denominator is not in form of 2m× 5n , So that gives us  non terminating recurring decimal expansion.


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Hope it helps u !!!

# Nikky