Question

Convert the following decimal number into fraction: $2.\;35$

Answer 1

Hint:We remove the decimal of the number and then we simplify the fraction into its smallest form. The upper part of the fraction is called numerator which will be the number without decimal and the lower part of the fraction is called the denominator which will be the zeros after removing the decimal.

Complete solution step by step:
Firstly we write down the given decimal number
$2.\;35$

The number has two digits after the decimal point and we know that decimal is called base ten positional numbers which means if there is one number after the decimal point we write 10 in the denominator after removing the dot and if it is two numbers we write 100 and so on.
$ \Rightarrow 2.35 = \dfrac{{235}}{{100}}$

So we have removed the decimal point successfully. Now our job is to simplify this fraction into its smallest form which is known as the irreducible form of a fraction when no number can divide both the numerator and denominator other than 1.

So for that we take highest common factor (HCF) of the two numbers of the fraction to see which number will divide both numerator and denominator i.e. HCF (235, 100) = Write down the factored form of both numbers and check for the highest common factor of the two.
$
\Rightarrow 235 = 5 \times 47 \\
\Rightarrow 100 = 2 \times 2 \times 5 \times 5 \\
$
As we can see only $5$ is the number which is common between the two
$ \Rightarrow {\text{HCF}}(235,100) = 5$

So we divide both numerator and denominator by $5$ and rewrite the fraction to get the simplest form of the fraction.

\[ \Rightarrow 2.35 = \dfrac{{235}}{{100}} = \dfrac{{\dfrac{{235}}{5}}}{{\dfrac{{100}}{5}}} =
\dfrac{{47}}{{20}}\]

This is the irreducible fractional form of the given number.

Note: Simplifying the fraction does not change the actual value of the fraction but it is written in the simplest form after simplification. Also the decimal number becomes an improper fraction because the numerator is greater in value than the denominator i.e. $47 > 20$.