Question

How do you write $8\% $ as a fraction and as decimal?

Answer 1

Hint: To convert the above question into a fraction, we need to remove the percent sign by dividing the given number by 100, and to convert it into decimal we need to put the decimal in the appropriate position after counting zeros present in the denominator.

Complete step-by-step answer:
As we know that when we remove $\% $ sign 100 will come in denominator, as we can see below.
$8\% = \dfrac{8}{{100}}$
As the denominator of 8 is 100, so we can easily convert the above fraction into decimal, because there are two zeros in the denominator so the decimal will be two places left.
$ = 0.08$
Hence, the decimal form of $8\% $ is $0.08$ .
Now, to convert $8\% $ into fraction we remove $\% $ sign and get 100 in denominator
$ = \dfrac{8}{{100}}$
Now, we will do factors of 8 and 100 to get reduced fraction
$ = \dfrac{{2 \times 2 \times 2}}{{5 \times 5 \times 2 \times 2}} \Rightarrow \dfrac{2}{{25}}$
As we observe that a pair of 2 are common in numerator and denominator, so we cancel them out and proceed with remaining factors.
$ = \dfrac{2}{{5 \times 5}} \Rightarrow \dfrac{2}{{25}}$
Hence, the fraction of $8\% $ is $\dfrac{2}{{25}}$ .

Note: We should remember that when the percentage sign removes then the number will get 100 at their denominator. We should also keep in mind that we should find out the reduced fraction which we can get after factorization.