Question

What is the value of $1.875$ in fractional form?

Answer 1

Hint: To convert the decimal value in its fractional form we will firstly convert the value in fractional form by removing the decimal and dividing the number with the 10 power equal to number after the decimal. Then we will divide both numerator and denominator with the same number till we get both of them as co-prime.

Complete step by step solution:
To find the fractional form of $1.875$ we will use the following steps:
Firstly we will remove the decimal sign and divide the number with 10 powers equal to the numbers after the decimal as follows:
$1.875=\dfrac{1875}{{{10}^{3}}}$
$1.875=\dfrac{1875}{1000}$………$\left( 1 \right)$
Now, as we can see both numerator and denominator of the above fraction have 5 and 0 in the end so that means it is divisible by 5.
On dividing equation (1) right side by 5 we get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{1875}{5}}{\dfrac{1000}{5}} \\
 & \Rightarrow \dfrac{375}{200} \\
\end{align}$
Again dividing above value by 5 we get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{375}{5}}{\dfrac{200}{5}} \\
 & \Rightarrow \dfrac{75}{40} \\
\end{align}$
Again dividing above value by 5 we get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{75}{5}}{\dfrac{40}{5}} \\
 & \Rightarrow \dfrac{15}{8} \\
\end{align}$
Now, as we can see that 15 and 8 are co-prime as they don’t have any same factor other than 1.
Hence, $1.875$ can be written in fractional form as $\dfrac{15}{8}$. This is improper fraction as the numerator is greater than denominator hence we write this fraction in simplified form as $1\dfrac{7}{8}$

Note: Two terms are used in the above solution i.e. Fraction and co-prime numbers. A fraction is a number that can be written in $\dfrac{a}{b}$ form where $a$ and $b$ is known as numerator and denominator respectively. Here a number $a$ is divided into $b$ equal parts. Two or more numbers are known as coprime if they don’t have any common factor other than 1. For example- 50 and 29 they don’t have any common factor other than 1.