Question

How do you convert $\dfrac{7}{20}$ as a decimal and a percent?

Answer 1

Hint: We are given a fraction which we have to express as a decimal and a percent as well. Firstly, we will divide 7 by 20 to give the quotient which will be in decimal form. We will find the decimal value with two decimal places. To find the percent of the given fraction, we will multiply the fraction by 100 and solve them to find the percent.

Complete step by step solution:
According to the given question, we will have to find both the decimal and the percent equivalent.
Decimal form involves the use of decimal point and we will find the decimal equivalent up to two decimal places.
The fraction we are given is,
\[7/20\]
Here, 20 is the divisor and 7 is the dividend. We will do the division, we have,
\[20\overset{0.35}{\overline{\left){\begin{align}
  & 7 \\
 & \underline{-0} \\
 & 70 \\
 & \underline{-60} \\
 & 100 \\
 & \underline{-100} \\
 & \_\_0\_ \\
\end{align}}\right.}}\]
We get the remainder as zero, that is 20 divides 7 completely.
The quotient we got after the division is the decimal equivalent of the given fraction.

Percent is the term we use to denote the amount in or for every hundred. If we are given a fraction, then we straightaway multiply the fraction by 100 to get the equivalent percent.
So, we have,
\[\dfrac{7}{20}\times 100\]
We know that, 100 is a multiple of 20 and so on cancelling we get the expression as,
\[\Rightarrow 7\times 5\]
Multiplying the above terms, we have,
\[\Rightarrow 35\]
Therefore, the decimal form is \[0.35\] and the percent equivalent is \[35\] percent.

Note: The decimal form can also be achieved without actually dividing but by doing certain modifications. We just have to make sure that the denominator is somehow made a multiple of 10. We have,
\[\dfrac{7}{20}\times \dfrac{5}{5}\]
\[\Rightarrow \dfrac{7\times 5}{20\times 5}\]
\[\Rightarrow \dfrac{35}{100}=0.35\] is the decimal form.
The percent can also be found by multiplying the decimal by 100. We get,
\[0.35\times 100=35\]
The percent equivalent is \[35\] percent.