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

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

Answer 2

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