Question

How do you change \[\dfrac{4}{{20}}\] into a Percent?

Answer 1

Hint: Percentage is defined as a ratio represented as a fraction of 100. If we have to find the percent of a number, then we will first divide the number by the total number and multiply it by 100. As we have to convert a fraction into a percentage we will simply multiply it by 100.

Formula Used:
Percentage is given by the formula \[P = \dfrac{x}{n} \times 100\] where \[x\] is the value for which the percentage is to be calculated and \[n\] is the total value.

Complete step by step solution:
We are given with a fraction \[\dfrac{4}{{20}}\]
Let \[\dfrac{x}{n} = \dfrac{4}{{20}}\].
We will convert the given fraction into a percent by using the Percentage formula \[P = \dfrac{x}{n} \times 100\]. So, multiplying the given fraction by 100, we get
\[P = \dfrac{4}{{20}} \times 100\]
Dividing 100 by 20, we get
\[ \Rightarrow P = 4 \times 5\]
By multiplying the terms, we get
\[ \Rightarrow P = 20\% \]

Therefore, the percentage of the given fraction \[\dfrac{4}{{20}}\] is \[20\% \].

Additional Information:
We know that Percent represents the number percent or the number per hundred and is represented by the symbol %. Percentages can be represented in the decimal form or in the fractional form. The percentage has no dimensions.

Note:
We can also convert the given fraction into a percent by equating the given fractions with the percent. Let \[\dfrac{x}{{100}}\] be the percent. Thus, we get
\[ \Rightarrow \dfrac{4}{{20}} = \dfrac{x}{{100}}\]
By rewriting the equation, we get
\[ \Rightarrow \dfrac{4}{{20}} \times 100 = x\]
By dividing the terms, we get
\[ \Rightarrow x = 4 \times 5\]
\[ \Rightarrow x = 20\% \]
Therefore, the percentage of the given fraction \[\dfrac{4}{{20}}\] is \[20\% \].
So, here we formed a linear equation and by solving the linear equation, we found out the Percent of the given number.