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
$$0.098={\displaystyle \frac{0.098\times 1000}{1000}}$$
Now we will solve the multiplication present in the numerator of the equation to get the number in the fraction form, we get
$$\Rightarrow 0.098={\displaystyle \frac{98}{1000}}$$
Dividing both numerator and denominator by the common factor 2, we get
$$\Rightarrow 0.098={\displaystyle \frac{49}{500}}$$
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 $${\displaystyle \frac{49}{500}}$$.

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., $$Numerator⩾Denominator$$. 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.