Question

How do you write $70\dfrac{1}{2}\% $ as a decimal and fraction?

Answer 1

Hint: We are given a percentage number in the form of mixed fraction and we have to find it in the form of fraction. And also in the decimal form. So first we will convert the mixed fraction percentage form into fraction form. Then into its decimal form. To convert into fraction form we will divide it by $100$ like this $ \dfrac{percentage}{100}$. As the percentage is not in its whole number form so we will reciprocal the divisor. Then simply reduce the fraction that much we can. For decimals we will use the non-reduced fraction form that is obtained and simply divide the numerator by the digit other than$100$and after that we will simply move the decimal point two places to the left and remove the percent sign.

Complete step-by-step answer:
Step1: We are given a percentage number i.e. $70\dfrac{1}{2}\% $. First we will find its fractional form for this first we will convert this mixed fraction into improper fraction. On converting we get:
$ \Rightarrow \dfrac{{\left( {70 \times 2} \right) + 1}}{2}$
On solving this we get:
$ \Rightarrow \dfrac{{141}}{2}\% $
Then we will divide this fraction by$100$hence we get:
$ \Rightarrow \dfrac{{141}}{2} \div 100$
Step2: As the percentage is not in whole number it is in fractional form so we will do the reciprocal of the divisor we get:
$ \Rightarrow \dfrac{{141}}{2} \times \dfrac{1}{{100}}$….(2)
As the numbers do not have a common factor in numerator and denominator so cannot be reduced further. And simply do the multiplication of fraction and obtained.
$ \Rightarrow \dfrac{{141}}{{200}}$
Step3: Now to convert it into decimal form we will use the expression (2)
$ \Rightarrow \dfrac{{141}}{2} \times \dfrac{1}{{100}}$
First we will divide the numerator by $2$ we will get:
$ \Rightarrow \dfrac{{70.5}}{{100}}$
As there are two zeroes in the hundred so we will move the decimal point two places to the left. And can remove the hundred from the denominator.
$ = 0.705$

Hence the fractional form is $\dfrac{{141}}{{200}}$ and decimal form is $0.705$

Note:
In such a type of question the solution of the question is easier in case of the whole number percentage but if we are given the percentage in fractions then we will first convert that mixed fraction into improper fraction then divide that fraction by 100 as ‘per’ in percentage means divided by 100. That's why we divide the fraction or whole number by 100 to remove the percentage. And to convert the percentage into decimal students mainly do the procedure again but this can be done only in one step by simply using the fraction produced and dividing the numerator by denominator. In the case of the whole number percentage just divide it by 100 and simply put the decimal point to two places left from the last digit.