Question

How do you express $0.64$ as a fraction in lowest terms?

Answer 1

Hint: In this question we will consider the fraction to be a variable $x$ and then we will multiply the number with a fraction to remove the decimal places in the number and then simplify it to get the required value of $x$.

Complete step-by-step answer:
We have the number given to us as: $0.64$.
We will consider the number to be $x$ therefore, it can be written as:
$\Rightarrow x=0.64$
Now in the term we have the number in decimal format with two places in the decimal.
Therefore, to remove the two decimal places we will multiply the number with $100$. Since the value of the number should not change, we will divide the number by $100$too.
On multiplying and dividing by $100$, we get:
$\Rightarrow x=0.64\times \dfrac{100}{100}$
Now on multiplying the terms, we get:
$\Rightarrow x=\dfrac{64}{100}$
Now this expression can be simplified by dividing both the terms by $4$, on simplifying, we get:
\[\Rightarrow x=\dfrac{16}{25}\]
Now this fraction cannot be reduced further therefore, it is the required fraction for the term $0.64$.

Note: It is to be remembered that whenever a value is added, subtracted, multiplied or divided on both the sides of the equation, the value of the equation does not change.
It is to be remembered that when a term which is in multiplication is transferred across the$=$sign, it has to be written as division. Same rule applies for addition and subtraction.
In the above question, we have a smaller number in the numerator and a larger number in the denominator. These types of fractions are called proper fractions. There also exist improper fractions which are the opposite of it.