Question

How do you convert $12\dfrac{3}{4}$ into a decimal and percent?

Answer 1

Hint: In this question, a mixed fraction number is given to us. We will first convert it into a proper fraction number. We know that fraction is defined as the ratio of two numbers. To convert the fraction to the decimal, we will simplify the fraction as much as possible. And To convert fraction to a percent, we need to multiply the fraction by 100 and reduce it to percent.

Complete step-by-step solution:
We are given the mixed fraction $12\dfrac{3}{4}$.
Converting it into a proper fraction, we get $12\dfrac{3}{4} = \dfrac{{\left( {12 \times 4} \right) + 3}}{2} = \dfrac{{51}}{4}$
First, we will convert it into decimal. To convert, we will simply divide the numerator by the denominator. Therefore, here we will divide 51 by 4.
$\dfrac{{51}}{4} = 12.75$
Thus, the decimal value of $12\dfrac{3}{4}$ is $12.75$.
Now, we will convert the fraction into percent. For this, we need to multiply the fraction by 100. Therefore, here, we will multiply $\dfrac{{51}}{4}$ by 100.
$\dfrac{{51}}{4} \times 100 = 1275\% $
Thus, the percent value of $12\dfrac{3}{4}$ is $1275\% $.

Note: Here, we have determined the percent and decimal values of the fraction separately. However, if we find the decimal value first then we can convert it into percent by simply multiplying it by 100. For example here, we have determined the decimal value of the fraction as $12.75$. Then, if we multiply it by 100, the value will be $12.75 \times 100 = 1275\% $ which is its percent value.

Similarly if we find the percent value first, then we can convert it into decimal by simply dividing it by 100. For example here, we have determined the percent value of the fraction as $1275\% $. Then, if we divide it by 100, the value will be $\dfrac{{1275}}{{100}} = 12.75$ which is its decimal value. Also, in $\dfrac{{51}}{4}$, the numerator is greater than the denominator. Therefore its decimal value is greater than one and its percent value is greater than hundred percent.