Question

The 2^n × 5^m" form of denominator 21/2 and its decimal expansion respectively are
(a) 2^0 x 5^1
(b) 2^1 x 5^1
(c) 2^0 x 5^0
(d) None of these​

Answer 1

Answer:

duydjgctucgjdjbcufgfhfuyfhif

Answer 2

Given:

Fraction $\frac{21}{2}$

To find:

$2^{n}$×$5^{m}$ form of the denominator and its decimal expansion.

Solution:

A fraction is terminating if its denominator is of the form $2^{n}$×$5^{m}$.

Here in $\frac{21}{2}$, the denominator is 2.

$2=2^{1}$×$5^{0}$

This is of the form $2^{n}$×$5^{m}$ and hence, the fraction is terminating.

Decimal expansion of $\frac{21}{2}=10.5$

Option (a) and (c) have $2^{n}$ as $2^{0}$. But, the answer we have deduced is $2^{1}$. Hence, both these options are incorrect.

In option (b), $5^{m}$ is given by $5^{1}$. But, in our answer, we have determined as $5^{0}$. Hence, this option is also incorrect.

∴ Option (d) is the suitable choice.

Final Answer

The correct form of denominator in $\frac{21}{2}$ is $2^{1}$×$5^{0}$ and its decimal expansion is given by $10.5$

The correct option is (d) None of these