Question

What is $3.25$ as a fraction?

Answer 1

Hint: We know that a number is called a fraction when it has a numerator and a denominator above and below the line that represents the operation division. As we know, the numbers that can be expressed as fractions are called rational numbers and they belong to the set of rational numbers. We will write the given decimal as the sum of two numbers in which one is a whole number and the other a decimal number.

Complete step-by-step solution:
Let us consider the given decimal number $3.25.$
We are asked to write the given decimal number as a fraction.
So, to write the given decimal number as a fraction, we need to write the given number as the sum of a whole number and a decimal number.
So, we will get $3.25=3+0.25.$
Now, we will convert the decimal number into a fraction.
For that, we will multiply and divide the number with $100$ for the given decimal number has two decimal positions.
And we will get $0.25={\displaystyle \frac{25}{100}}.$
Now, this is a fraction and free from the decimal point and the decimal positions.
We will now simplify the fraction to get ${\displaystyle \frac{25}{100}}={\displaystyle \frac{1}{4}}.$
And now the given decimal number and the sum will become $3.25=3+{\displaystyle \frac{1}{4}}.$
Now, we will take LCM and we will get $3.25={\displaystyle \frac{12+1}{4}}={\displaystyle \frac{13}{4}}.$
Hence the required fraction is ${\displaystyle \frac{13}{4}}.$

Note: As we know, we can find the fraction even without splitting the number as the sum of two numbers. When we multiply the given decimal number with ${\displaystyle \frac{100}{100}},$ we will get $3.25\times {\displaystyle \frac{100}{100}}.$ And we will get ${\displaystyle \frac{325}{100}}.$ We know that $25\times 13=325$ and $25\times 4=100.$ So, we will get ${\displaystyle \frac{13}{4}}.$