Question

How do you write $24\% $ as a fraction & as a decimal ?

Answer 1

Hint:
This is a problem in which the student has to bring the percentage into a fraction in its simplest form. This can be treated as a problem in fraction in which the first step would be to convert percentage into a fraction by dividing it by $100$. After the first step the student has to find the greatest common multiple for both the numerator and denominator, or the student can also bring both the numbers in its simplest form i.e in terms of prime number multiplication. Third step would be to cancel out the common multiples .This would be the final answer. If the student wants to convert the number to a decimal, one trick is by converting them to nearest $100s$. By doing this the student will not have to sit and divide the numerator and the denominator. Chances of going wrong are also very less. First step is to find the nearest $100s$. After that the student has to multiply numerator and denominator by the same number so that the denominator has $100$ or it’s multiple. After this step the student will just have to input the decimal point to get the final answer.

Complete step by step solution:
First step is to convert the given percentage in the form of a fraction
$24\% = \dfrac{{24}}{{100}}.........(1)$
Second step is to bring numerator and denominator in terms of its prime factors.
$\dfrac{{24}}{{100}} = \dfrac{{2 \times 2 \times 2 \times 3}}{{5 \times 5 \times 4}}..........(2)$
From the above step we can see that the fraction has the greatest common multiple$4$. Striking off the common multiple we get the fraction in its simplest form.
$\dfrac{{24}}{{100}} = \dfrac{6}{{25}}.........(3)$
Thus, the simplest form of the fraction is $\dfrac{6}{{25}}$
Now, to convert the given number to a decimal form. In this particular sum we will be using equation $1$ as it is already having the denominator as $100$. Since the denominator is $100$, we will not have to multiply by any other number. Thus the answer would now be obtained by just putting a decimal point before $24$

Thus the decimal value for $\dfrac{{24}}{{100}}$ is $0.24$.

Note:
Only important step in this sum is to first bring the percentage into a fraction and then in terms of its prime factors. Sometimes when the complicated sum like $40\% \times \dfrac{5}{{20}} \times \dfrac{4}{{40}}$it is advisable that the student first converts all the terms into the form of a fraction and then cancel out common terms after which, he/she should reduce the remaining terms to its the prime factors .For decimal form the students are always advised to bring the numerator in terms of its nearest $100th$ multiple and then convert the number to decimal. Chances of making an error by following this method are negligible compared to direct division.