Question

What is the decimal value of $\dfrac{3}{50}$?

Answer 1

Hint: In this problem we need to convert the given fraction into decimal value. Decimal value means the value which is having a decimal point before non-zero integers or digits in the value. It will be easier to convert a fraction into decimal value when we have multiples of $10$ in the denominator. So, we will first observe the denominator of the given fraction and try to convert it into multiples of $10$ like $10,100,1000,....$ by using some mathematical operations. After getting denominators as multiples of $10$, place a decimal point for the numerator before $n$ digits from the right side where $n$ is the number of zeros in the denominator.

Complete step by step solution:
The fraction is $\dfrac{3}{50}$.
We can observe that the numerator of the given fraction is $3$, and the denominator of the given fraction is $50$.
To convert the given fraction into decimal value we are going to convert the denominator into multiples of $10$.
We have $50$ as a denominator, in order to convert $50$ into the nearest multiple of $10$ which is $100$, we need to multiply the number $50$ with $2$.
So, multiplying and dividing the given fraction with $2$, and do not changing the value of the given fraction, then we will get
$\dfrac{3}{50}=\dfrac{3}{50}\times \dfrac{2}{2}$
Multiplying the values in numerator with numerator and denominator with denominator, then we will have
$\begin{align}
  & \dfrac{3}{50}=\dfrac{3\times 2}{50\times 2} \\
 & \Rightarrow \dfrac{3}{50}=\dfrac{6}{100} \\
\end{align}$
From the above equation we have the fraction $\dfrac{6}{100}$ as an equivalent fraction for the given fraction $\dfrac{3}{50}$.
Considering the fraction $\dfrac{6}{100}$.
In the above fraction we have the denominator as $100$. So, it is very easy to convert it into decimal value. In $100$ we have $2$ zeros, so we need to place the decimal point before two digits from right in the numerator. But we have a one digit numerator which is $6$. In order to convert the fraction into decimal we are going to place another zero before $6$, then we will get
$\dfrac{3}{50}=\dfrac{6}{100}=0.06$

Hence the decimal value of the given fraction $\dfrac{3}{50}$ is $0.06$.

Note: In this problem we have used to convert the denominator of the given fraction into multiples of $10$ to convert the fraction into decimal value. We also have another method to convert the fractions into decimal values which is a long division method. In this method we will divide the numerator with the denominator by considering the decimal value.