Question

Express the following fraction as decimals correct to four decimal places. Then, express the decimals as percentage:
$$4/7$$

Answer 1

Hint: We are given a fraction and we are asked to express the given fraction as decimal correct to four decimal places. Then, using the decimal we are asked to express the obtained decimal to percentage. Firstly, we will divide the numerator 4 by the denominator 7 using the long division method. We will continue the division correct to four decimal places and we will have the decimal equivalent of the given fraction as the quotient. Then, using this decimal equivalent we will multiply the decimal by 100 to get the percentage equivalent of the given fraction. Hence, we will have the required values.

Complete step by step answer:
According to the given question, we are given a fraction and we are asked in the question to express the given fraction as decimal and afterwards express it as percentage as well.
The fraction that we have is,
$${\displaystyle \frac{4}{7}}$$
Now, we will carry out the division operation of the above fraction using the long division method and we have to get the decimal equivalent correct to four decimal places.
We have,
$$7\stackrel{0.5714}{\stackrel{―}{)\begin{array}{rl}& 4\\ & \underset{―}{-0}\\ & 40\\ & \underset{―}{{\displaystyle \frac{-35}{\begin{array}{rl}& 50\\ & \underset{―}{-49}\\ & 10\\ & \underset{―}{-7}\\ & 30\\ & \underset{―}{-28}\\ & 2\end{array}}}}\end{array}}}$$
So, we have the decimal equivalent of the given fraction as,
$${\displaystyle \frac{4}{7}}=0.5714$$
Now, we have to express the decimal equivalent that we obtained as percentage.
In order to express a decimal to equivalent we just have to multiply the decimal by 100 and so we have,
$$0.5714\times 100=57.14\mathrm{\%}$$
Therefore, the percentage equivalent to the given fraction is $$57.14\mathrm{\%}$$
Therefore, we have, $${\displaystyle \frac{4}{7}}=0.5714=57.14\mathrm{\%}$$

Note: The long division method should be done carefully without missing any terms or adding extra zeros after the decimal point. Also, the percentage should not be complicated by adding additional denominator or numerator to it, that is, if we have the decimal equivalent of a fraction we can straightaway write its percentage by multiplying it with 100.