Question

How do you write 3.71 as a percentage?

Answer 1

Hint: We recall the definition of percentage as fraction of 100 or ratio to 100. We convert any number into a percentage by multiplying 100. We use the working rules for decimal multiplication with 100 and shift the decimal point 2 places towards the right of $3.71$ to get the percentage.

Complete step by step answer:
We know that percentage is derived from the word per centum in Latin which means per hundred. The percentage in mathematics is a number or ratio expressed as a fraction of 100. We denote the percentage of $p$ as $p\%$ where ‘%’ is a symbol of percentage. If we say $p\%$of $x$ that means if we divide $x$ into hundreds we can allocate $p$ in each of the hundred, for example $45\%$ of 200 means we can allocate 45 for each hundred in 200. We can calculate $p\%$ of $x$ as the total allocation $y$ as
\[y=\dfrac{p}{100}\times x\]
So when we convert a number say $n$ to percentage we have to multiply and divided by 100 to get the allocation and then put percentage sign per hundred as
\[n=n\times \dfrac{100}{100}=\dfrac{n\times 100}{100}=\left( n\times 100 \right)\%\]
We are asked to convert the number $3.71$ into percentages. So we multiply 100 to $3.71$ and then put a percentage sign after the product. We know how to multiply decimal numbers with numbers of type $10,100,1000,...$. We have shifted the decimal point towards right as many as places equal to the numbers zeros after 1. So we multiply $3.71\times 100$ we have to shift the decimal point which is in between 3 and 7 towards fro 2 digits since there are two zeros in 100 to get
\[3.71\times 100=371.\]
We know we can omit the decimal point if there are no non-zero digits after the decimal point. So we omit the decimal point and put percentage sign behind to have
\[3.71\times 100=371\%\]

Note:
If we have $a$ number of elements and there are total $b$ number of elements then we can express $a$ as a percentage $p$ of $b$ using the working rule $p=\dfrac{a}{b}\times 100$. We use percentage to compare quantities where denominator is the same for example we can compare exam marks better with percentage than ratios because the total exam mark is same for each student.