Question

How do you convert \[\dfrac{4}{7}\] to a decimal?

Answer 1

Hint: In the given question, we have been asked to convert a fraction into a decimal. If the fraction has a negative sign in front of it. For solving that, we simply divide the numerator by the denominator, and after calculating the result, and if the fraction has a negative sign, just attach the negative sign in the front of the value.

Complete step by step answer:
We have to change \[4/7\] into decimal.
First, we divide the numerator \[\left( 4 \right)\] by the denominator \[\left( 7 \right)\].
\[7\mathop{\left){\vphantom{1\begin{array}{l}{\rm{ }}4{\rm{ }}.{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0\\\dfrac{{3{\rm{ }}5{\rm{ }}}}{\begin{array}{l}{\rm{ }}5{\rm{ }}0\\{\rm{ }}\dfrac{{4{\rm{ }}9}}{\begin{array}{l}{\rm{ }}1{\rm{ }}0\\{\rm{ }}0{\rm{ }}7\end{array}}\end{array}}\end{array}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}{\rm{ }}4{\rm{ }}.{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0{\rm{ }}0\\\dfrac{{3{\rm{ }}5{\rm{ }}}}{\begin{array}{l}{\rm{ }}5{\rm{ }}0\\{\rm{ }}\dfrac{{4{\rm{ }}9}}{\begin{array}{l}{\rm{ }}1{\rm{ }}0\\{\rm{ }}0{\rm{ }}7\end{array}}\end{array}}\end{array}}}}
\limits^{\displaystyle\,\,\, {0.571}}\]
So, \[4/7 = 0.\overline {571428} \]
Now, we put a bar on the \[571428\], because the digit keeps repeating infinitely, and it is to represent the same thing only – the digit(s) is repeating infinite times, i.e., it is a non-terminating repeating decimal.

Additional Information:
For solving the fraction into a decimal, we just divide the numerator by the denominator. But, if we have to calculate the reverse – convert a decimal to fraction, we first count the number of digits after the decimal point; let it be ‘c’. Then we take the complete number without the decimal point as the numerator and make the denominator equal to \[1\] followed by \[c\] zeroes.

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. When the numbers are
divided, care must be taken as that is the point where the mistakes happen.