Question

Express the following as a fraction in simplest form: $0.7$

Answer 1

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 $0.7$
The number has one digit after 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 so we have
$0.7 = \dfrac{7}{{10}}$
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 (7, 10) = Write down the factored form of both numbers and check for the highest common factor of the two.
$\Rightarrow 7 = 7 \times 1 \\\ \Rightarrow 10 = 2 \times 5 \\\$
As we can see there is no number which is common between the two
${\text{HCF}}\left( {7,10} \right) = 1$
This means that the fraction $\dfrac{7}{{10}}$ is already in the simplest form i.e. irreducible which cannot be reduced further.

Note: Simplifying the fraction does not change the actual value of the fraction but it is written in the simplest form after simplification and our number was already in that form. Also the decimal number becomes a proper fraction because the numerator is lesser in value than the denominator i.e. $7 < 10$.