Question

What is decimal of $6\dfrac{1}{2}\%$?

Answer 1

Hint: In this problem we need to calculate the decimal value of the given value. We can observe that the given values have mixed fraction along with the percentage symbol. So, we will first consider the mixed fraction and convert it into normal fraction. We know that the normal fractional form of a mixed fraction which is in the form $a\dfrac{b}{c}$ is given by $\dfrac{ac+b}{c}$. By using this phenomenon, we will convert the given mixed fraction into normal fraction after that we will consider the percentage symbol. In order to convert a percentage value into fraction we will divide the percentage value with $100$. From the fraction with denominator $100$ we can place the decimal point before two digits in the numerator to get the decimal value.

Complete step-by-step solution:
Given value, $6\dfrac{1}{2}\%$.
Consider the mixed fraction in the given value which is $6\dfrac{1}{2}$.
We know that the fractional form of a mixed fraction which is in the form of $a\dfrac{b}{c}$ is given by $\dfrac{ac+b}{c}$. From this we can write the mixed fraction $6\dfrac{1}{2}$ as
$6\dfrac{1}{2}=\dfrac{6\times 2+1}{2}$
Simplifying the above value, then we will get
$\begin{align}
  & 6\dfrac{1}{2}=\dfrac{12+1}{2} \\
 & \Rightarrow 6\dfrac{1}{2}=\dfrac{13}{2} \\
\end{align}$
Now substitute the above value in the given value $6\dfrac{1}{2}\%$, then we will get
$6\dfrac{1}{2}\%=\dfrac{13}{2}\%$
To remove the percentage symbol in the above value, dividing the whole value with $100$, then we will get
$6\dfrac{1}{2}\%=\dfrac{\left( \dfrac{13}{2} \right)}{100}$
We know that the value of $\dfrac{13}{2}$ is $6.5$. Substituting this value in the above equation, then we will get
$6\dfrac{1}{2}\%=\dfrac{6.5}{100}$
In the above value we have $100$ in denominator, so to get the decimal value of the above value we are going to place the decimal value before two digits from right in the numerator. We can observe that the in numerator we have already decimal value. So, we are going to move the decimal point to two digits from its place. We can also observe that there is only one digit before the decimal. So, we need place zeros where there are required that means we need to shift decimal by two digits, but there is only one digit is present before the decimal, so we are going to place a zero before the digit $6$, then we will get
$6\dfrac{1}{2}\%=0.065$
Hence the decimal value of the given value $6\dfrac{1}{2}\%$ is $0.065$.


Note: In this problem while converting the fraction having denominator $100$ into decimal value we have placed the decimal before the two digits from right side if you have $10$ in the denominator then we need to place the decimal before one digit from right and if you have $1000$ in the denominator then we need to place the decimal before three digits likewise we need to place decimal point.