Question

How do you write the fraction \[\dfrac{2}{3}\] as a \[{\text{decimal?}}\]

Answer 1

Hint: In the question\[,\] we have given a number that is in fraction either that is a positive fraction or negative fraction. Also\[,\] either that is a proper fraction or improper fraction. We have to convert the given fraction to decimal. We have to write the fractional number that is equivalent to the decimal.

Complete step by step solution:
The given question is to write the given fractional number in decimals. That means we have to write that decimal number which is equivalent to the given fractional number. Fractional number is nothing but that which can be written in the form of \[\dfrac{p}{q}\] where \[q \ne 0\]
This fraction can be positive or negative. Also the fraction can be proper fraction or improper fraction.
Now\[,\] we have to convert \[\dfrac{2}{3}\] to the decimal which can be possible if we divide \[2{\text{ by }}3.\] Here \[2\] will be the dividend and \[3\] will be the divisor.
\[3\mathop{\left){\vphantom{1{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{2}}}}}}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{{\dfrac{\begin{gathered}
  20 \\
  18 \\
\end{gathered} }{2}}}}}}}}}
\limits^{\displaystyle \,\,\, {.666}}\]

When we divide \[2{\text{ by }}3.\] since \[2\] is less than \[3.\] Therefore in the quotient\[,\] we use point which is decimal and as a result of this \[10\] is multiplied by \[2.\] Now dividend is \[20.\] so when \[20\] is divided by \[3.\] we got \[2\] as remainder and \[0.6\] as quotient. Again decimal is there in the quotient. Then we can again multiply \[10\] by the remainder. Hence \[2\] becomes\[20.\] Now when\[20\] is divided by \[3.\] We get \[6\] in the quotient and \[2\] is left as remainder. Now quotient becomes \[0.66.\] Again decimal is there in the quotient\[,\] Therefore remainder becomes \[20.\] when \[20\] is divided by \[3\] We get remainder \[2\] and \[0.666\] in the quotient. And hence the quotient is \[0.666\]
Therefore \[\dfrac{2}{3}\] fraction is equal to \[0.666\] in the decimal.

Note: The question was about to convert fraction to decimal. Since the given fraction is a proper fraction because the numerator is smaller than the denominator. Since dividend is smaller than divisor. Then we took decimal in the quotient and \[10\] is multiplied by the divisor each and every time after one division.