Question

The decimal representation of \[\dfrac{{11}}{{{2^3} \times 5}}\] will
(a) terminate after 1 decimal place
(b) terminate after 2 decimal places
(c) terminate after 3 decimal places
(d) not terminate

Answer 1

Hint: Here in this question, we have to simplify the given term and we have to the number in the decimal form. While writing the number in decimal form we have to check whether it is a terminating decimal or non-terminating decimal, if it is a terminating means we have to see at which place the decimal value will be terminated.

Complete step-by-step answer:
The given question is in the form of fraction and we have to convert it into decimal form.
Fractions are the numerical values that are a part of the whole. If a number or a thing is divided into equal parts, then each part will be the fraction of the whole. A fraction is denoted as \[\dfrac{a}{b}\] , where a is the numerator and b is the denominator.
In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fraction’s part is called the decimal point.
Now consider the given question
 \[ \Rightarrow \dfrac{{11}}{{{2^3} \times 5}}\]
The given is in the form of fraction and in the denominator the term is in the form of exponent first we simplify the exponent term and then we simplify the fraction
On simplifying the exponent term, we have
 \[ \Rightarrow \dfrac{{11}}{{8 \times 5}}\]
On multiplying the number 8 and 5 we get 40, so now we have
 \[ \Rightarrow \dfrac{{11}}{{40}}\]
On dividing the 11 by 40 we get 0.275.
Therefore, we get 0.275, it will get terminated after 3 decimal places. Therefore the ( C ) is the correct one.
So, the correct answer is “Option C”.

Note: The number can be converted from one form to the other form. For the conversion of numbers, we have some rule or method. By using the specific methods and rules we can convert the number. The fraction number has a numerator and denominator. The percentage is represented by the symbol %. The decimal number will have the decimal point. Terminating decimals: these have a finite number of digits after the decimal point.