Question

How do you write \[0.098\] as a fraction?

Answer 1

Hint: Here we will first remove the decimal number by multiplying and dividing the multiple of 10 to it. Then we will divide the numerator and denominator by a common factor to simplify it further and get the required answer.

Complete step by step solution:
Given number is \[0.098\].
First, we will remove the decimal from the given number. So, to remove the decimal from the given number we will multiply and divide the given number by 1000. Therefore, we get
\[0.098 = \dfrac{{0.098 \times 1000}}{{1000}}\]
Now we will solve the multiplication present in the numerator of the equation to get the number in the fraction form, we get
\[ \Rightarrow 0.098 = \dfrac{{98}}{{1000}}\]
Dividing both numerator and denominator by the common factor 2, we get
\[ \Rightarrow 0.098 = \dfrac{{49}}{{500}}\]
As there is no common factor between the numerator and denominator, we cannot simplify it further.

Hence, a fraction of \[0.098\] can be expressed as \[\dfrac{{49}}{{500}}\].

Note:
We know that there are three main types of fractions i.e. proper fractions, improper fractions, and mixed fractions.
Proper fractions are a fraction having the numerator less, or lower in degree, than the denominator i.e., \[Numerator < Denominator\]. The value of proper fraction after simplification is always less than 1.
Improper Fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction i.e., \[Numerator \geqslant Denominator\]. After the simplification of an improper fraction results in the value which is equal or greater than 1, but not less than 1.
A mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1. An improper fraction can be converted into a mixed fraction.