Question

How do you convert \[\dfrac{22}{55}\] into a percent and decimal?

Answer 1

Hint:
Let a fraction be \[\dfrac{p}{q}\] where p and q are coprime. If the p, q is not coprime then we have to make them coprime by the elimination of the factors common in both the numerator and denominator. This fraction can be converted into a decimal by making the denominator of the fraction form into multiples of 10. This fraction can be converted into percent form by multiplying its decimal form with 100.

Complete step by step answer:
According to the given question, we are given a number in the form of \[\dfrac{p}{q}\]. Let it be taken as ‘a’ = \[\dfrac{22}{55}\].
Here, we can see that 22 and 55 are not coprime. The reason is, by factorization, we can write 22 as \[2\times 11\] and 55 as \[5\times 11\]. Both the numbers have 11 in common.
Hence, ‘a’ as a rational number is \[\dfrac{2}{5}\]. Now,
1) Conversion into decimal: -
In a = \[\dfrac{2}{5}\], the denominator is 5. 5 can be made into a multiple of 10 by multiplying with 2. So, on multiplying numerator and denominator with 2, we get \[\dfrac{4}{10}\] which is simply 0.4
2) Conversion into percent: -
We got the decimal as \[\dfrac{4}{10}\]. So, the percent will be \[\dfrac{4}{10}\times 100\] which equals 40%.
Hence, the decimal and percent form of \[\dfrac{22}{55}\] are 0.4 and 40% respectively.

Note:
 we can do the conversion of a fractional number into a decimal by simply dividing the numerator of the fraction form with the denominator. We can also do the conversion of a fraction into a percent by multiplying it by 100 and then simple division.
While calculating decimal form we must round the decimal part.