Question

Find after how many places of decimal the decimal form of the number 27/2^3.5^4.3^2 will terminate

Answer 1

Digits after decimal in decimal expansion of $\frac{27}{2^3\:5^4\:3^2}$ is 4.

Step-by-step explanation:

To find : After how many places of decimal the decimal form of the number  $\frac{27}{2^3\:5^4\:3^2}$ will terminate ?

Solution :

Re-write expression as,

$\frac{27}{2^3\:5^4\:3^2}=\frac{3^3}{2^3\:5^4\:3^2}$

Using law of exponent, $\frac{x^a}{x^b}=x^{a-b}$

$=\frac{3^{3-2}}{2^3\:5^4}$

$=\frac{3}{2^3\:5^4}$

Now find value of each exponent

$=\frac{3}{8\,.625}$

$=\frac{3}{5000}$

$=0.0006$

Therefore, Digits after decimal in decimal expansion of $\frac{27}{2^3\:5^4\:3^2}$ is 4.

#Learn more

Find after how many places of decimal the decimal form of the number 27/ 2cube . 5 to the power of 4

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Answer 2

Answer: Digits after decimal in decimal expansion is 4 .