Question

How do you express $ 475\% $ as a decimal and as a mixed number or fraction in the simplest form?

Answer 1

Hint: To convert the percentage in the form of decimals, we must divide it by \[100\] which gives us the decimal equivalent of the percentage. To convert the percentage in the form of fraction first convert the percentage in the form of number with the denominator with base hundred and then remove common factors from the numerator and the denominator for the simplified form of fraction. Also, if the numerator is bigger than the denominator then convert it into the mixed fraction. Let us apply the above concepts for the given expression.

Complete step-by-step answer:
Take the given expression
 $ 475\% $
To convert the given percentage in the form of decimals place $ 475 $ over one hundred.
 $ = \dfrac{{475}}{{100}} $ .... (A)
Now, to get the decimal number, place the decimal point and move two points from right to left since we have two zeros in the denominator.
 $ = 4.75 $ ... (B)
So, the correct answer is “$ 4.75 $”.

Take expression (A)
 $ \dfrac{{475}}{{100}} $
Find the factors in the numerator and the denominator.
 $ = \dfrac{{25 \times 19}}{{25 \times 4}} $
Common factors from the numerator and the denominator cancel each other. Therefore remove $ 25 $ from the numerator and the denominator.
 $ = \dfrac{{19}}{4} $
Since the numerator is bigger than the denominator we will divide the numerator with the denominator. Convert the given mixed fraction in the form of fraction.
Mixed number is the combination of a whole number and the fraction. Fraction is the number expressed in the form of the numerator and the denominator.
 $ = 4\dfrac{3}{4} $ ... ©
Expression (B) and (C) are the required solutions.
So, the correct answer is “$ 4\dfrac{3}{4} $”.

Note: Always remember that percentage is always based off $ 100\% $ so the decimals up to the hundredths place will always be integers and the numbers after the hundredths place will be after the decimal and the tens place in the percentage will always be in the tenths place in the decimal form as well.