find after how many places of decimal the decimal form of the number 27/2^3.5^4.3^2 will terminate
Answers
Answer:
Digits after decimal in decimal expansion of is 4
Step-by-step explanation:
Given Expression is
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,
using law of exponent
Now find value of each exponent
Therefore, Digits after decimal in decimal expansion of is 4
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