Question

How do you convert \[\dfrac{8}{{50}}\] to a decimal?

Answer 1

Hint: This is the given number in fraction form. It is having a numerator and denominator. As we need to convert it in decimal we will perform the division as 8 divided by 50. We will write the denominator in terms of multiple of 10 so that we can divide 8 by 5 and then the answer is divided by 10 such that the decimal point will be shifted just one place to the left.

Complete step by step solution:
Given that \[\dfrac{8}{{50}}\].This is a fraction. Now we can write the denominator as
\[\dfrac{8}{{5 \times 10}}\]
Separating two fractions we get,
\[\dfrac{8}{5} \times \dfrac{1}{{10}}\]
On dividing 8 by 5 we get,
\[5\mathop{\left){\vphantom{1\begin{gathered}
  8 \\
   - 5 \\
  {\bar 3} \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  8 \\
   - 5 \\
  {\bar 3} \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, 1}\]
Now for 3 to be remainder we will take a decimal point in the quotient such that it adds a zero to the remainder.
\[5\mathop{\left){\vphantom{1\begin{gathered}
  8 \\
   - 5 \\
  \bar 3\bar 0 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  8 \\
   - 5 \\
  \bar 3\bar 0 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {1.}}\]
Now we will divide 30 by 5 such that
\[5\mathop{\left){\vphantom{1\begin{gathered}
  8 \\
   - 5 \\
  \bar 3\bar 0 \\
   - 30 \\
  \bar 0\bar 0 \\
\end{gathered} }}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{gathered}
  8 \\
   - 5 \\
  \bar 3\bar 0 \\
   - 30 \\
  \bar 0\bar 0 \\
\end{gathered} }}}
\limits^{\displaystyle \,\,\, {1.6}}\]
This completes the division as the remainder is zero. Now we can write the fraction as,
\[1.6 \times \dfrac{1}{{10}}\]
On dividing with 10 the decimal shifts,
\[0.16\]

So we can write \[\dfrac{8}{{50}} = 0.16\].

Note: Here note that we are given with a fraction in the form of numerator and denominator. The decimal form is a number with a decimal point. If the numerator is smaller than the denominator then we call it a proper fraction. Note that we cannot divide 8 by 50 so we converted 50 as a product in the form of 10. And then the fraction so formed can be easily divided.