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# Convert the following into percentage: $\dfrac{5}{{12}}$

Last updated date: 21st Jul 2024
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Answer
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Hint: First we have to define what the terms we need to solve in the problem are. Percentage formula is used to find the share or amount of something in terms of $100$. The percentage formula is given by:
Percentage = given value divided by total value $\times 100$

Complete step-by-step solution:
Fraction consists of Numerator which is written above the line and denominator which is written below the line. The numerator indicates a number of equal parts, and the denominator indicates how many of those parts make up a whole. The denominator of a fraction can never be zero because zero parts can never make up a whole.
Since we need to find the percentage value from the fractions.
The following steps are followed to convert fraction to percent:
Step1: Convert the given fraction into equivalent decimal number
Step2: The obtained decimal number is multiplied by 100, to get the required percent value.
Now we solve the given problem as per the above steps:
Fractions which have a denominator that is a factor of 100 are easy to write as percent.
For those where denominator is not a factor of 100, you can change it to a decimal first by dividing
$\dfrac{5}{{12}} = 0.416666...$
This can be written as a fraction with 100 as the denominator: $\dfrac{{41.6666...}}{{100}}$= $41.6666...\%$
However, the recurring decimal $.6666....$ is equal to $\dfrac{2}{3}$
Therefore $41.6666...\%$= $41\dfrac{2}{3}\%$
The same result will be obtained by multiplying the fraction by $100\%$
$\dfrac{5}{{12}} \times 100\% = 41.6666...\% = 41\dfrac{2}{3}\%$

Note: Fractions are converted to their equivalent decimal number using the following;
The numerator of fraction is divided by its denominator and the quotient obtained after division is the decimal equivalent of a given fraction. Finding the percentage is very easy by multiplying the fraction directly with 100 as percentage means the part out of 100.