G-5 After how many places of docimal
the decimal from of number sy
will terminate ?
23x543
no
ry.r,
Onclusive of all )
Answers
Answer:
g
Step-by-step explanation:
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Step-by-step explanation:
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