Answer

Verified

454.8k+ views

**Hint:**We will use the fact that every rational number with denominator of the form ${2^m} \times {5^n}$ will always be terminating. Then, we will try to make powers of 10 in the denominator by multiplying and dividing with some numbers, so that we can get a decimal easily and know its place.

**Complete step-by-step answer:**

Let us first understand the meaning of terminating rational numbers:

A terminating decimal is a decimal with a certain number of digits to the right of the decimal point. Examples include 3.2, 4.075, and -300.12002. All of these are rational. In simpler words, it means that if a number ends at some point after decimal, it is terminating.

Now, coming back to the question:

We have: $\dfrac{{43}}{{{2^4} \times {5^3}}}$. It has ${2^4} \times {5^3}$ in its denominator.

We know that every rational number with denominator of the form ${2^m} \times {5^n}$ will always be terminating.

Hence, $\dfrac{{43}}{{{2^4} \times {5^3}}}$ is terminating as well.

Now, consider the denominator for once.

Denominator = \[{2^4} \times {5^3} = ({2^3} \times {5^3}) \times 2 = {10^3} \times 2\].

Hence, the number given to us becomes $\dfrac{{43}}{{{2^4} \times {5^3}}} = \dfrac{{43}}{{2 \times {{10}^3}}}$.

We can multiply and divide the number by 5, it would not make any difference because we are eventually multiplying the number by 1 because of multiplying and dividing by the same number.

So, $\dfrac{{43}}{{{2^4} \times {5^3}}} = \dfrac{{43}}{{2 \times {{10}^3}}} \times \dfrac{5}{5}$.

Simplifying it, we will have with us:-

$\dfrac{{43}}{{{2^4} \times {5^3}}} = \dfrac{{43 \times 5}}{{{{10}^3} \times 2 \times 5}} = \dfrac{{215}}{{{{10}^3} \times 10}} = \dfrac{{215}}{{{{10}^4}}}$

Hence, $\dfrac{{43}}{{{2^4} \times {5^3}}} = \dfrac{{215}}{{10000}} = 0.0115$.

Hence, it terminates after 4 digits.

Hence, the answer is 4 digits.

**Note:**The students might make the mistake of just dividing the number as per their requirements but forgetting to multiply it as well to nullify any changes in the number.

The students also might forget to check in the start whether the number given to them is actually terminating or it is just a trick question. So, remember to check the conditions for that as well.

Always remember that all rational numbers may not be terminating. For example: $\dfrac{1}{3}$ and our most known number $\pi $ that is equal to $\dfrac{{22}}{7}$.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The states of India which do not have an International class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you graph the function fx 4x class 9 maths CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Name the three parallel ranges of the Himalayas Describe class 9 social science CBSE