Question

How do you write $ 0.95\% $ as a fraction in simplest form?

Answer 1

Hint:Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from a certain size whereas the percentage is the number or ratio expressed as a fraction of hundred. Know the difference between the fraction and the percentage and apply accordingly.

Complete step by step solution:
Take the given expression: $ 0.95\% $
It can be expressed as –
 $ = \left( {\dfrac{{0.95}}{{100}}} \right) $
To convert decimal into fraction, place the decimal number over its place value. There are two digits after decimal point, for $ 0.95 $ since $ 95 $ is in the hundredths place so that we place $ 95 $ over
 $ 100 $ to create the equivalent fraction i.e. $ \dfrac{{95}}{{100}} $ .

Simplify the above equation –

 $ = \left( {\dfrac{{95}}{{10000}}} \right) $
Find the factors of the above expression –
 $ = \left( {\dfrac{{19 \times 5}}{{100 \times 20 \times 5}}} \right) $
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.

 $ = \left( {\dfrac{{19}}{{100 \times 20}}} \right) $
Simplify the above equation –
 $ = \left( {\dfrac{{19}}{{2000}}} \right) $

This is the required solution.

Note:Convert the decimal point in the form of fraction. To convert decimal into fraction, place the decimal number over its place value. For example, for $ 0.6 $ the six is in the tenths place so that we place $ 6 $ over $ 10 $ to create the equivalent fraction i.e. $ \dfrac{6}{{10}} $ and similarly if there is two digits after decimal point, for $ 0.06 $ the six is in the hundredths place so that we place $ 6 $ over $ 100 $ to create the equivalent fraction i.e. $ \dfrac{6}{{100}} $ . Be good in multiples and division and since it is most important to find the factors and to remove common factors in the fraction to get the equivalent simplified fraction.