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  • Without actually performing the long division, find if 987by10500 will have terminating or non-terminating decimal expansion give reason for your answer

Without actually performing the long division, find if 987/10500 will have terminating or non-terminating decimal expansion give reason for your answer.

Answers (1)

We can also write this number as
:\frac{987}{10500}= \frac{3\times 7\times 47}{3\times 7\times 2^{2}\times 5^{3}}= \frac{47}{2^{2}\times 5^{3}}

= \frac{47}{2^{2}\times 5^{3}}\times \frac{2}{2}= \frac{47\times 2}{5^{3}\times 2^{3}}
= \frac{94}{\left ( 10 \right )^{3}}= \frac{94}{1000}= 0\cdot 094
Here, we have a finite number of digits after the decimal point.
 Hence it is terminating decimal expansion.
 

Posted by

infoexpert27

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