Question

What is $2.25$ as a fraction?

Answer 1

Hint: We will write the decimal number as a sum of a whole number and a decimal number that is less than $1.$ Then, we will find the fraction form of the decimal number. And then, we add the numbers by taking LCM.

Complete step by step solution:
Let us consider the given decimal number $2.25.$
We are asked to find this decimal number as a fraction.
For finding the corresponding fraction, we need to write the given decimal number as the sum of a whole number and a decimal number that is less than $1.$
We can write the given decimal number as the sum of a fraction and decimal number less than $1$ as $2.25=2+0.25.$ We know that $0.25$ is a decimal number less than $1.$
Now, we need to find the fraction equivalent to the decimal number $0.25.$
Let us multiply and divide this number with $100$ to get $\dfrac{25}{100}.$
We know that the product of $25$ and $4$ is $100.$
That is, $25\times 4=100.$
From this, we will get the fraction as $\dfrac{25}{4\times 25}.$
Let us cancel $25$ from both the numerator and the denominator.
We will get $\dfrac{1}{4}.$
So, the given decimal number can be written as the sum of a whole number and a fraction.
We will get $2.25=2+\dfrac{1}{4}.$
Let us take LCM to find the sum in the form of a fraction.
We will get $2.25=\dfrac{\left( 2\times 4 \right)+1}{4}=\dfrac{9}{4}.$

Hence the given decimal number is equivalent to the fraction $\dfrac{9}{4}.$

Note: Even if we do not write the given decimal number as a sum, we can find the fraction by multiplying and dividing the given decimal number with $100.$ We will get $2.25=\dfrac{225}{100}.$ When we divide both numerator and denominator with $25,$ we will get the fraction $\dfrac{9}{4}.$