Question

Express \[0.08\% \] as a fraction
a.\[\dfrac{1}{{250}}\]
b.\[\dfrac{1}{{1250}}\]
c.\[\dfrac{1}{{125}}\]
d.\[\dfrac{1}{{25}}\]

Answer 1

Hint: Here, we will use the definition of fraction to convert the given percentage. Fraction is considered to be the ratio of two numbers i.e. fraction has numerator and denominator. So, we will first express the percentage as a fraction. Then we will convert the given number into the simplest fraction by dividing it with the LCM.

Complete step-by-step answer:
As we all know that we can write \[0.08\% \] as \[0.0008\]
We have to write the given number in the form of fraction
$\Rightarrow$ \[0.0008 = \dfrac{{0.0008}}{1}\]
We need to remove the decimal so we will multiply the denominator with a number so to make it a whole number.
Multiplying both numerator and denominator by 10000, we get
$\Rightarrow$ \[0.0008 = \dfrac{8}{{10000}}\]
Now we have to simplify the above fraction. So, to simplify the equation we have to find the LCM(Least Common Multiple) of both numerator and denominator i.e. 8 and 10000
So, 8 is the LCM of 8 and 10000
Now dividing both numerator and denominator by 8, we get
$\Rightarrow$ \[0.0008 = \dfrac{{8/8}}{{10000/8}} = \dfrac{1}{{1250}}\]
$\Rightarrow$ \[\dfrac{1}{{1250}}\] is the simplest fraction of the \[0.08\% \]
\[\therefore\] Option B is the correct answer.

Note: We converted the decimal number into fraction. There are three main types of fraction i.e. proper fractions, improper fractions and mixed fractions.
(i)Proper fraction is a fraction having the numerator less, or lowers in degree, than the denominator.
i.e., Numerator < Denominator
The value of proper fraction after simplification is always less than 1.
(ii)Improper Fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction.
i.e., Numerator ≥ Denominator
After the simplification of an improper fraction results in the value which is equal or greater than 1, but not less than 1.
(iii)Mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1.
Also we should know how to find the LCM (Least Common Multiple) of the numbers. LCM is the smallest positive integer that is divisible by both the numbers.