Question

How do you convert \[\dfrac{3}{8}\] into a decimal and percent?

Answer 1

Hint: We solve this by simple division. If the numerator term is less than the denominator term we put a decimal point next to the number we write zeros. In general we know that remainder in a division is something which is ‘left over’ or ‘remaining’. Using this we can find decimals of a fraction. When the obtained decimal or fraction is multiplied by ‘100’ we get the percent and it is demoted by \[\% \] .

Complete step-by-step answer:
Given, \[\dfrac{3}{8}\] so by short division method,
First we have \[8|\underline {3.0{\text{ }}0{\text{ }}0{\text{ }}0{\text{ }}} \]
It does not matter because we put a decimal point there.
Since 3 is less than 8 so write the decimal point giving, so we have 30 instead of 3, so
 \[\
  8|\underline {3.0{\text{ }}0{\text{ }}0{\text{ }}0{\text{ }}} \\
  {\text{ }}0. \\
\ \]
8 is less than 30 so we know \[3 \times 8 = 24\] which is nearer to 30. So we have a remainder 6 and we keep it on one side,
 \[\
  8|\underline {3.0{\text{ }}0{\text{ }}0{\text{ }}0{\text{ }}} {\text{ remainder 6}} \\
  {\text{ }}0.3{\text{ }} \\
\ \]
Thus we have 60, we know \[7 \times 8 = 56\] which is nearer to 60. So we have a remainder 4 and we keep it on one side,
 \[\
  8|\underline {3.0{\text{ }}0{\text{ }}0{\text{ }}0{\text{ }}} {\text{ remainder 4}} \\
  {\text{ }}0.3{\text{ }}7{\text{ }} \\
\ \]
Thus we have 40 now, we know \[5 \times 8 = 40\] and we don’t have any remainder or remainder is equal to zero.
 \[\
  8|\underline {3.0{\text{ }}0{\text{ }}0{\text{ }}0{\text{ }}} \\
  {\text{ }}0.3{\text{ }}7{\text{ }}5{\text{ }} \\
\ \]
Since there are no remainder we stop here.
Thus we have, \[ \Rightarrow \dfrac{3}{8} = 0.375\] . That is decimal form.
So, the correct answer is “ \[ 0.375 \] ”.

Now to find the percentage we need to multiply the obtained decimal with 100.
 Percent \[ = 0.375 \times 100\]
 \[ = 37.5\% \] . That is the percentage.
So, the correct answer is “ \[ 37.5\% \] ”.

Note: In above to find the percent we can multiply the fraction into 100. That is \[\dfrac{3}{8} \times 100\] . But we already know the \[\dfrac{3}{8}\] value so we simply multiplied it. In above if we have kept on getting remainder while solving we can stop up to certain digits. Know the tables from 1 to 20. Which will help to solve this kind of problem easily.