Question

How do you convert $\dfrac{4}{{13}}$ to a decimal?

Answer 1

Hint: Here we will convert the given fraction into a decimal. So that we have to use long division methods to get the decimal answer. After doing some simplification we get the required answer.

Complete step-by-step solution:
Sometimes we are not able to find an equivalent fraction which has $10,100$ or $1000$ as the denominator. In these cases, we need to divide the numerator by the denominator.
Given fraction is $\dfrac{4}{{13}}$,
Now we are going to divide the numerator by denominator and complete the division. Here our denominator is greater than the numerator.
Usually in division we can easily divide the numbers if the denominator is less than the numerator. But in this division we can’t divide easily. We will do some extra steps to divide the numerator.
Here our divider is $13$ and dividend is $4$, now using long division method, until the remainder is zero or repeats,
\[\begin{array}{*{20}{c}}
  {\,\,\,\,\,0.307692} \\
  {13)\overline {4.\,\,00\,0\,0\,0\,0} } \\
  {\underline {3.9\,\,} \,\,\,\,\,\,} \\
  {\,\,\,\,1\,0\,0} \\
  {\,\,\,\,\,\,\,\underline {91} } \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,90} \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\underline {78} } \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,120} \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline {117} } \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,30} \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline {26} } \\
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4}
\end{array}\]
Now we are going to divide $4$ by $13$, here our divider $13$ is greater than our dividend $4$, so the quotient becomes a decimal number. It starts with a point.
We can add zeros into the dividend for each remainder which is less than the divider.
In this particular problem the remainder repeats, returning to the original dividend $4$ so the pattern $3,0,7,6,9,2$ will repeat indefinitely, we can stop in the certain process.
$\dfrac{4}{{13}} = 0.307692...$
Now we are getting the decimal number of the fraction by using a long division method.

Therefore the value of $\dfrac{4}{{13}}$ is $0.307692...$

Note: We know that when the number obtained by dividing by the denominator is the decimal form of the fraction. There can be two situations in converting fractions to decimals. When division stops after a certain number of steps as the remainder becomes zero. When division continues as there is a remainder after every step.