Question

The Decimal Expansion Of The Rational Number 14587 By 1250 Will Terminate After how many decimal places ?

Answer 1

Answer: 4

Step-by-step explanation:

Factorising 1250, we'll get 5⁴ × 2. The total number of decimal places is the highest power of 5 or 2. So the answer is 4.

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Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

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★ To Find :

We have to find that, after how many places will $\sf{\frac{14587}{1250}}$ will terminate.

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★ Solution :

Firstly, we will make factors of 14587 and 1250.

factorisation of 14587

$\begin{array}{r | l} 29 & 14587 \\ \cline{1-2} 503 & 503 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Factorization of 1250

$\begin{array}{r | l} 2 & 1250 \\ \cline{1-2} 5 & 625\\ \cline{1-2} 5 & 125 \\ \cline{1-2} 5 & 25 \\ \cline{1-2} 5 & 1 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

$\sf{→ \frac{14587}{1250}} \\ \\ \sf{→ \frac{29 \times 503}{2 \times 5 \times 5 \times \times 5 \times 5}} \\ \\ \bf{Multiplying \: in \: numerator \: and \: denominator \: by \:2^3.}\\ \\ \sf{→ \frac{29 \times 503}{2 \times 5 \times 5 \times \times 5 \times 5} \times \frac{2^3}{2^3}} \\ \\ \sf{→ \frac{116696}{10000}} \\ \\ \Large{\implies{\boxed{\boxed{\sf{11.6696}}}}}$

$\therefore$ It will terminate after 4 digits.