Math, asked by bahubali38, 1 year ago

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

Answers

Answered by aquialaska
212

Answer:

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

Step-by-step explanation:

Given Expression is \frac{27}{2^3\:5^4\:3^2}

To find: No of Digits after decimal in terminating decimal expansion of given expression.

Terminating decimal expansion of rational nos.

⇒ Given expression ia a rational no.

To find No of digits after decimal in decimal expansion, we first simplify the rational no.

Consider,

\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

Answered by umeshtiwari80
11

Answer:-

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

2

3

5

4

3

2

27

is 4

Step-by-step explanation:

Given Expression is \frac{27}{2^3\:5^4\:3^2}

2

3

5

4

3

2

27

To find: No of Digits after decimal in terminating decimal expansion of given expression.

Terminating decimal expansion of rational nos.

⇒ Given expression ia a rational no.

To find No of digits after decimal in decimal expansion, we first simplify the rational no.

Consider,

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

2

3

5

4

3

2

27

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

2

3

5

4

3

2

3

3

using law of exponent \frac{x^a}{x^b}=x^{a-b}

x

b

x

a

=x

a−b

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

2

3

5

4

3

3−2

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

2

3

5

4

3

Now find value of each exponent

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

8.625

3

=\frac{3}{5000}=

5000

3

=0.0006=0.0006

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

2

3

5

4

3

2

27

is 4

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