Question

How do you convert ${\displaystyle \frac{5}{7}}$ into a decimal and percent?

Answer 1

Hint: We will convert a fraction into a decimal by simply long division method, where we will take the decimal because 5 or less than 5 is not available in the table of 7, and then to convert in percentage we will multiply decimal form with 100.

Complete step by step solution:
First of all, we will convert ${\displaystyle \frac{5}{7}}$ into decimal. Which we can do by long division method.
$$\begin{gathered} 7\stackrel{{\displaystyle 0.714285}}{)\phantom{15.000000 \\ {\displaystyle \frac{49}{10 \\ {\displaystyle \frac{07}{30 \\ {\displaystyle \frac{28}{20 \\ {\displaystyle \frac{14}{60 \\ {\displaystyle \frac{56}{40 \\ {\displaystyle \frac{35}{5}} \\ }} \\ }} \\ }} \\ }} \\ }} \\ }\stackrel{―}{\phantom{1}5.000000 \\ {\displaystyle \frac{49}{10 \\ {\displaystyle \frac{07}{30 \\ {\displaystyle \frac{28}{20 \\ {\displaystyle \frac{14}{60 \\ {\displaystyle \frac{56}{40 \\ {\displaystyle \frac{35}{5}} \\ }} \\ }} \\ }} \\ }} \\ }} \\ }} \end{gathered}$$
As we can see in the above division that 5 or less than 5 is not available in the table of 7 so we will start quotient with decimal and take decimal at the end of dividend. Now we can extend any number of zeros after decimal as we write in the dividend $5.000000$ . We will start division where we know that $7\times 7=49$ , and we subtract 49 from dividend $50-49=1$ , 1 will be remainder, which will become new dividend after one zero will take from dividend, 1 become 10, similarly $7\times 1=7$ and we subtract 7 from dividend $10-7=3$ , one more zero will take from dividend and 3 become 30, $7\times 4=28$ , $30-28=2$ , again 2 become 20, $7\times 2=14$ , $20-14=6$ , and 6 become 60, $7\times 8=56$ , $60-56=4$ , and remainder 4 become 40, $7\times 5=35$ , $40-35=5$ , 5 remainder shows that remainder repeats, now we will stop division, because quotient will also repeat.

Decimal form of the $${\displaystyle \frac{5}{7}}\Rightarrow 0.\overline{714285}$$
Now, we will convert it in percentage by multiplying decimal form with 100
${\displaystyle \frac{5}{7}}\Rightarrow 71.\overline{4285}\mathrm{\%}$

Note: We should keep remembering that when our remainder starts repeating we should stop dividing and place a bar on the repeating digits because when the remainder repeats, the quotient will also repeat.