Question

Express $0.08\%$ as a fraction. Which one of the following is the correct answer?
A. $\dfrac{1}{250}$
B. $\dfrac{1}{1250}$
C. $\dfrac{1}{125}$
D. $\dfrac{1}{25}$

Answer 1

Hint: First we will define what a fraction is. Then we will first convert the decimal into a fraction, for that we will write the given number as numerator while removing the decimal point and then in the denominator, we will write as many as zeroes to the right of $1$ as there are digits in the decimal part. Finally we will convert $\%$ by writing $100$ in the denominator in its place and then finally after simplifying we will get our fraction.

Complete step by step answer:
First of all, we will understand what is a fraction? So a fraction is a number we need for measuring. For counting, we have the natural numbers: $1,2,3,4.....$ . But when we need to measure something for example, length, it will not always be a whole number. Therefore, we need numbers that are less than $1$ that means the numbers that are the parts of $1$ : half of $1$, a third , a fifth etc.
In simpler terms, let’s take one-third for an example. It is represented as: $\dfrac{1}{3}$ , means 1 out of 3. The numerator of $\dfrac{1}{3}$ is $1$ and the denominator is $3$. They are called the terms of the fraction. The denominator shows the number of equal parts into which number $1$ has been divided. The numerator shows how many of those parts we selected. For example, in the example above: $\dfrac{1}{3}$, since the denominator is $3$, $1$ is divided into $3$equal parts and we selected one part out of it as shown in figure below:

In converting the decimals to fractions, we know that decimal can always be converted into a fraction by using the following steps:
First we will obtain the decimal given in the question that is: $0.08\%$, We will now remove the decimal points from the given decimal and take it as numerator and at the same time in the denominator, we will write as many as zeroes to the right of $1$ as there are digits in the decimal part as shown below:
$0.08\%\Rightarrow \dfrac{8}{100}\%$,
We will now also put a $100$ in the denominator in the place of $\%$ sign, therefore, $\dfrac{8}{100}\%=\dfrac{8}{100}\times \dfrac{1}{100}=\dfrac{8}{10000}$ .
We will now simplify the given fraction by dividing both numerator and denominator by $8$ :
$\dfrac{8}{10000}=\dfrac{\left( \dfrac{8}{8} \right)}{\left( \dfrac{10000}{8} \right)}=\dfrac{1}{1250}$
Therefore, $0.08\%=\dfrac{1}{1250}$.
So, the correct answer is “Option B”.

Note: In many cases like these, we may forget to convert the percent sign after converting the decimal part into fraction. Always remember to replace the percent sign and put 100 in its place in the denominator. While simplifying, see what number is common between them and can be used to divide them.