Question

Convert the given fraction into percentage. $\dfrac{2}{7}$

Answer 1

Hint: Now we know that to convert the fraction in percentage we want 100 in denominator. The most general way of solving this question is to write the given fraction in decimal form. Now multiply by 100. The number we obtain is the percentage representation of the given fraction.

Complete step by step answer:
Now first let us understand what fractions are.
Fractions are real numbers of the form $\dfrac{p}{q}$ where p and q are both integers such that q is not equal to zero.
But what does $\dfrac{p}{q}$ represent.
Now $\dfrac{p}{q}$ actually means p parts of q.
For example consider the given example.
Now imagine you have 6 chocolates, and I took 2 from those.
Now this means I took 2 out of 6 chocolates
Hence I took $\dfrac{2}{6}$ chocolate from you.
Now we can write this fraction in simple form that is in a form such that the numerator and denominator are co-prime (do not have common factors)
Hence we write $\dfrac{2}{6}=\dfrac{1}{3}$
Now percentages are nothing but a special form of fractions.
Percentages are fractions with 100 in denominators.
Hence if we want to represent $\dfrac{1}{2}$ in percentage we will multiply numerator and denominator by 50 and hence we get $\dfrac{1\times 50}{2\times 50}=\dfrac{50}{100}$ hence we say it is equal to 50 percent.
Now the most general method of writing fractions is to convert it into decimals and then multiply by 100.
For example $\dfrac{1}{2}=0.5$ and 0.5 × 100 = 50.
Now consider the given fraction $\dfrac{2}{7}$
Converting it into fraction we get $\dfrac{2}{7}=0.2857$
Now multiplying by 100 we get 28.57

Hence $\dfrac{2}{7}=28.57\%$

Note: Note that when we write the fraction in decimal form we have the denominator as 1.
For example $\dfrac{1}{2}=\dfrac{0.5}{1}$ . Now consider multiplying the numerator and denominator by 100. Then we get $\dfrac{0.5\times 100}{1\times 100}=\dfrac{50}{100}$ hence we get a fraction with 100 in the denominator that is nothing but percentage. Note if the denominator is factor of 100 then we need not convert it into fraction we can multiply appropriate number to make it a fraction with denominator 100.