Question

How do you write $\dfrac{{21}}{{16}}$ as a decimal ?

Answer 1

Hint: In order to write the given fraction as decimal, we need to divide the given numerator with the denominator. If we have a remainder and the numerator part is over, then we add a decimal point and continue to divide until our remainder becomes zero. The quotient that we find then becomes our answer.

Complete step-by-step solution:
The given fraction is $\dfrac{{21}}{{16}}$. Now we need to present this number as a decimal, thus we divide the numerator with the denominator as shown below:
$\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,1} \\
  {16)\overline {21} } \\
  {\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,5}
\end{array}$
 We get a remainder as $5$, but in order to make it a decimal, we need to keep dividing until the remainder becomes zero or reaches a periodic set of repeating numbers. Thus, we add a decimal point $\left( \bullet \right)$ to the quotient and add zero to the remainder. On adding zero to the remainder, it becomes $50$. Now, we need to find a multiple of $16$ closest to $50$ to divide it with. We find that $16 \times 3 = 48$, which is the closest number. Thus, we divide it as so:
$\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,1.3} \\
  {16)\overline {21\,} } \\
  {\,\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,\,50} \\
  {\,\,\,\,\underline { - 48} } \\
  {\,\,\,\,\,\,\,2}
\end{array}$
We get the remainder as $2$, we continue dividing until we get zero as the remainder. We add zero to two and now the remainder becomes $20$, we need to find a multiple of $16$ closest to $20$. We find $16 \times 1 = 16$ to be the closest thus:
\[\begin{array}{*{20}{c}}
  {\,\,\,\,1.31} \\
  {16)\overline {21} } \\
  {\,\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,\,50} \\
  {\,\,\,\,\underline { - 48} } \\
  {\,\,\,\,20} \\
  {\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,4}
\end{array}\]
Now, we have the remainder as $4$. We divide it again with $2$ after adding zero to $4$ and getting $40$ thus:
$\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,1.312} \\
  {16)\overline {21} } \\
  {\,\,\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,50} \\
  {\,\,\,\,\underline { - 48} } \\
  {\,\,\,\,20} \\
  {\,\,\,\underline { - 16} } \\
  {\,\,\,\,40} \\
  {\,\,\,\underline { - 32} } \\
  {\,\,\,8}
\end{array}$
 We get the remainder as $8$. We need to divide it further to get the remainder as zero. Since we have a decimal point in the quotient, therefore we can add a zero to $8$ and make it$80$. We know that $16 \times 5 = 80$, so we divide the remaining number with $5$ so as to get our remainder as zero.
$\begin{array}{*{20}{c}}
  {\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,1.312} \\
  {16)\overline {21} } \\
  {\,\,\,\,\,\underline { - 16} } \\
  {\,\,\,\,\,50} \\
  {\,\,\,\,\underline { - 48} } \\
  {\,\,\,\,20} \\
  {\,\,\,\underline { - 16} } \\
  {\,\,\,\,40} \\
  {\,\,\,\underline { - 32} } \\
  {\,\,\,80}
\end{array}} \\
  {\,\,\,\underline { - 80} } \\
  {\,\,\,0}
\end{array}$

Now that we have our remainder as $0$, our required decimal is: $1.3125$.

Note: Decimal numbers are those numbers which have two parts to them separated by a dot, the number to the left of the dot represents whole numbers, whole numbers to the right of the dot represent fractional parts. The ‘dot’ is also known as the decimal point. The numbers after the decimal point are less than $1$ . There are different kinds of decimal numbers, such as:
Recurring decimal numbers:
These numbers have repeating numbers after the decimal point. They may be finite or infinite.
Example:
$3.125125$ (finite)
$1.6262626$ (infinite)
Non-repeating decimal numbers:
These numbers do not have a repeating decimal part.
Example: $\pi = 3.14159....$