Question

How do you convert $\frac{1}{3}$ into a decimal and percent?

Answer 1

Converting $\frac{1}{3}$ into a decimal and percent:

Step 1: Converting into $\frac{1}{3}$ decimal:

If we apply the long division method in the division of $1$ by $3$, we get the quotient as: $0.33333333333...$ i.e. a repeating pattern has been observed (after the decimal point $3$ is repeating infinitely many times).

The mathematical way to show the repeating process is to put a bar over the last $3$ that we write.

Thus, we get: $\frac{1}{3}=0.3\overline{3}$.

Step 2: Converting $\frac{1}{3}$ into percentage:

We know that the equivalent percentage of the fraction$\frac{a}{b}$ is $\frac{a}{b}\times 100\%$.

Here, we get:

$$\begin{gathered} \frac{1}{3}\times 100\% \\ =0.3\overline{3}\times 100\% \\ =33.3\overline{3}\% \end{gathered}$$

Therefore, $\frac{1}{3}=0.3\overline{3}$ and $\frac{1}{3}=33.3\overline{3}\%$.