Question

How do you convert $\dfrac{6}{8}$ into decimal & as a percent?

Answer 1

Hint:
First step is to convert to the simplest form and then 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. Now after converting the given number to decimal, we will use a step prior to the final answer to convert to fraction having denominator as $100$ to percentage form.

Complete step by step solution:
First step is to bring numerator and denominator in terms of its prime factors.
$\dfrac{6}{8} = \dfrac{{2 \times 3}}{{2 \times 4}}..........(2)$
From the above step we can see that the fraction has the greatest common multiple$2$. Striking off the common multiple we get the fraction in its simplest form.
$\dfrac{6}{8} = \dfrac{3}{4}.........(3)$
Thus, the simplest form of the fraction is $\dfrac{3}{4}$
Now, to convert the given number to a decimal form. In this particular sum we will be using the equation $3$. Now in order to bring the denominator in terms of $100s$, we will have to multiply by numerator and denominator by $25$.
$\dfrac{3}{4} = \dfrac{3}{4} \times \dfrac{{25}}{{25}}........(4)$
From equation, now the new fraction is $\dfrac{3}{4} = \dfrac{{75}}{{100}}..........(5)$
The the value of $\dfrac{6}{8}$ in decimal form is $0.75$
Using the equation $5$ to convert the number in percent form.
Thus in order to convert to percentage form we will have to multiply equation $5$ by $100$

Thus $\dfrac{6}{8}$ in percent form is $75\% $

Note:
Only important step in this sum is to first bring the fraction in terms of its prime factors and then getting the denominator in terms of its nearest $100s$. 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. Also to bring the number in percentage form the student should not forget to multiply the fraction by$100$.