Question

After how many decimal places the decimal expansion of 37/2^3×5^4 will terminate?

Answer 1

Answer: After 4 places

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Answer 2

The decimal expansion of $\frac{37}{2^3\times 5^4}$ will terminate after 4 decimal places.

Step-by-step explanation:

Given : Expression $\frac{37}{2^3\times 5^4}$

To find : After how many decimal places the decimal expansion of expression will terminate?

Solution :

Expression $\frac{37}{2^3\times 5^4}$

Multiply and divide by 2,

$\frac{37}{2^3\times 5^4}=\frac{37\times 2}{2^4\times 5^4}$

$\frac{37}{2^3\times 5^4}=\frac{74}{(2\times 5)^4}$

$\frac{37}{2^3\times 5^4}=\frac{74}{(10)^4}$

$\frac{37}{2^3\times 5^4}=0.0074$

i.e. the decimal expansion of $\frac{37}{2^3\times 5^4}$ will terminate after 4 decimal places.

#Learn more

The decimal expansion of rational number 53/2^4×5^3 will terminate after how many decimal places.

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