Question

What kind of decimal expansion does 37/8 have?

Answer 1

when we divide 37by 8 we get 4.625

and have terminatting decimal expansion

Answer 2

$Given \: fraction \: \frac{37}{8}$

$= \frac{37}{2^{3}}\: \blue { (2^{n} \times 5^{m} \:form )}$

$= \frac{37\times 5^{3}}{2^{3}\times 5^{3}}$

$= \frac{37\times 125}{(2\times 5)^{3}}$

$= \frac{4625}{(10)^{3}}$

$= \frac{4625}{1000}$

$= 4.625 \: \pink{ ( Terminating \: decimal )}$

Therefore.,

$\red{ \frac{37}{8}} \green { = 4.625 \: \pink{ ( Terminating \: decimal )}}$

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