Question

How do you convert \[0.4\% \] into a fraction and decimal?

Answer 1

Hint: Here, we will use the definition of a fraction to convert the given percentage. We will first divide the given percentage by 100 to convert it into fraction form. We will then multiply and divide the fraction by a suitable multiple of 10 to remove the decimal. Then we will divide the numerator and denominator of the fraction by a common factor to get the fraction in its simplest form. We will then divide the numerator by the denominator to get the required decimal conversion of the percentage.

Complete step by step solution:
The given number is \[0.4\% \].
First, we will convert the given number from the percentage form to the normal fraction form. We know that to convert the percentage into the normal form we will divide the number by 100. Therefore, we get
\[0.4\% = \dfrac{{0.4}}{{100}}\]
Now we will remove the decimal from the numerator of the fraction form. So, we will multiply both numerator and denominator by 10. Therefore, we get
\[ \Rightarrow 0.4\% = \dfrac{{0.4 \times 10}}{{100 \times 10}}\]
\[ \Rightarrow 0.4\% = \dfrac{4}{{1000}}\]
Now here, we can see that there is a common factor between the numerator and denominator of the above fraction.
So, dividing the numerator and denominator by 4, we get
\[ \Rightarrow 0.4\% = \dfrac{1}{{250}}\]
Hence the fraction form of the given percentage is \[\dfrac{1}{{250}}\].
Now to convert the given percentage into decimal form, we will divide 1 by 250. Therefore, we get
\[ \Rightarrow 0.4\% = 0.004\]

Hence the given percentage in the decimal form is equal to \[0.004\].

Note:
While calculating the percentage of something we have to multiply the ratio by 100 to get it in terms of percentage. However, to convert the percentage into a normal form we will divide the number by 100. The percentage of a variable is equal to the ratio of the value of the variable to the total value of the variable and multiplies it with 100 to get the required percentage of the variable. The concept of the percentage is used for the representation of the larger set of data having very large values like for population increase or used in our educational system or used in banks for interest rates. We should put the % sign after writing the percentage value.