Write 8/3 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Understand the Problem
The question is asking to convert the fraction 8/3 into a decimal form, indicating any repeating digits if necessary.
Answer
$2.\overline{6}$
Answer for screen readers
The decimal form of $\frac{8}{3}$ is $2.\overline{6}$.
Steps to Solve
- Divide 8 by 3
To convert the fraction $\frac{8}{3}$ into decimal form, divide the numerator (8) by the denominator (3).
- Perform long division
When you divide 8 by 3:
- 3 goes into 8 two times (because $3 \times 2 = 6$).
- Subtract $6$ from $8$, which gives you a remainder of $2$.
- Bring down a zero to make it $20$.
- Continue the division
Now divide:
- 3 goes into 20 six times ($3 \times 6 = 18$).
- Subtract $18$ from $20$, which gives a remainder of $2$ again.
- Bring down another zero to make it $20$ once more.
- Identify the repeating decimal
You can see that you keep getting $20$ each time after bringing down a zero. This results in the same steps repeating. Hence, we denote the repeating digit with a bar.
The result will be $2.\overline{6}$ where $6$ is the repeating digit.
The decimal form of $\frac{8}{3}$ is $2.\overline{6}$.
More Information
The decimal representation $2.\overline{6}$ indicates that the digit $6$ repeats indefinitely. This means that $\frac{8}{3}$ is not a terminating decimal and demonstrates the concept of repeating decimals.
Tips
- Forgetting to indicate the repeating part with a bar.
- Miscalculating the long division, especially when dealing with remainders.
