Question

Express the following ratio as percentages:
 \[17:20\]

Answer 1

Hint: First we have to know the ratio of two quantities \[a\] and \[b\] in the same units, is the fraction of two quantities i.e., \[\dfrac{a}{b}\] and we write it as \[a:b\] . In the ratio \[a:b\] , we call \[a\] as the first term or antecedent and \[b\] , the second term or consequent. Then convert the ratio into fraction \[\dfrac{a}{b}\] . Multiply the fraction by \[100\] and put the percentage sign ( \[\% \] ).

Complete step-by-step answer:
A percentage is a number or ratio expressed as a fraction of \[100\] . It is often denoted using the percent sign, " \[\% \] ", although the abbreviations " \[pct.\] " and sometimes " \[pc\] " are also used.
By a certain percent, we mean that many hundredths. Thus, \[x\] percent means \[x\] hundredths, written as \[x\% \] . To find the percentage of a number two cases arises. When the number is in decimal form, you just need to multiply the decimal number by \[100\] . For example, to convert \[0.25\] to a percentage, \[0.25 \times 100 = 25\% \] . The second case involves a fraction. If the given number is in fractional form, first convert it to a decimal value and multiply by \[100\] .
Given \[17:20\] --(1)
Then the fraction is \[\dfrac{{17}}{{20}}\]
So, multiply the fraction by \[100\] and put the percentage sign, we get
 \[\dfrac{{17}}{{20}} \times 100 = 85\% \]
Hence the first number is \[85\% \] of the second number.
So, the correct answer is “ \[85\% \] ”.

Note: Note that the multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio. The proposition is the equality of two ratios. A percentage from Latin per centum "by a hundred".