Question

express the denominator of 23÷20 in the form of 2^n×5^m and state whether the given fraction is Terminating or non Terminating repeating decimal
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Answer 1

Given:

Expression 23 $\div$ 20.

To find:

Denominator in the form of $2^n\times 5^m$ and finding whether the given fraction is terminating or non terminating repeating decimal.

Solution:

The denominator of 23 $\div$ 20 is 20.

Let us factorize 20 now:

$20 = 4 \times 5\\20 = 2 \times 2 \times 5\\20 = 2 ^2 \times 5^1$

Now, let us compare factors of 20 with $2^n\times 5^m$.

$2^n\times 5^m$ = $2^2 \times 5^1$

$\Rightarrow n =2, m = 1$

So, 20 can be represented as $2^2 \times 5^1$.

Let us learn what are terminating fractions and non terminating repeating decimal.

Terminating fractions mean the form $\frac{p}{q}$ which can be completely divided and  can be represented in decimal form.

For example:

$\dfrac{5}{2} = 2.5$

Non terminating repeating decimal mean the form $\frac{p}{q}$, when represented in decimal form, the division does not get terminated and there is a repeating digit.

For example:

$\dfrac{10}{3} = 3.333333......\\OR\\\dfrac{10}{3} = 3.\overline3$

Here, 3 is the repeating number.

Given fraction is:

$\dfrac{23}{20} =1.15$

$\therefore$ The given fraction is terminating.

Answer 2

The denominator 20 in the form of $2^{n}\times 5^{m}$ is $2^{2}\times 5^{1}$.

Step-by-step explanation:

We have to express the denominator of 23 ÷ 20 in the form of 2^n × 5^m.

As it is clear that 20 is the denominator of the given fraction. So, finding the factors of 20 by using prime factorization method we get;

20 = 2 $\times$ 10

10 = 2 $\times$ 5

5 = 5 $\times$ 1

So, the factors of 20 = 2 $\times$ 2 $\times$ 5 = $2^{2}\times 5^{1}$.

If we compare this with the form of $2^{n}\times 5^{m}$, we can observe that the value of n = 2 and that of m = 1.

So, the denominator 20 in the form of $2^{n}\times 5^{m}$ is $2^{2}\times 5^{1}$.

The given fraction  $\frac{23}{20}$ is terminating because when we divide this fraction we get the value of 1.15 which represents that the decimal expansion is terminating after two decimal points.