Question

How do you convert $\dfrac{5}{7}$ 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 $\dfrac{5}{7}$ into decimal. Which we can do by long division method.
\[7\mathop{\left){\vphantom{1
  5.000000 \\
  \dfrac{{49}}{
  {{ }}10 \\
  \dfrac{{{{ }}07}}{
  {{ }}30 \\
  \dfrac{{{{ }}28}}{
  {{ }}20 \\
  \dfrac{{{{ }}14}}{
  {{ }}60 \\
  \dfrac{{{{ }}56}}{
  {{ }}40 \\
  \dfrac{{{{ }}35}}{5} \\
 } \\
 } \\
 } \\
 } \\
 } \\
 }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{
  5.000000 \\
  \dfrac{{49}}{
  {{ }}10 \\
  \dfrac{{{{ }}07}}{
  {{ }}30 \\
  \dfrac{{{{ }}28}}{
  {{ }}20 \\
  \dfrac{{{{ }}14}}{
  {{ }}60 \\
  \dfrac{{{{ }}56}}{
  {{ }}40 \\
  \dfrac{{{{ }}35}}{5} \\
 } \\
 } \\
 } \\
 } \\
 } \\
 }}}
\limits^{\displaystyle \,\,\, {0.714285}}\]
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 \[\dfrac{5}{7} \Rightarrow 0.\overline {714285} \]
Now, we will convert it in percentage by multiplying decimal form with 100
$\dfrac{5}{7} \Rightarrow 71.\overline {4285} \% $

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.