Write 8/3 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
The Correct Answer and Explanation is:
To write 83\frac{8}{3}38 as a decimal, you need to divide 8 by 3. Let’s go through the steps of this long division process:
- Start by dividing 8 by 3.
8÷3=28 \div 3 = 28÷3=2 with a remainder of 2.
So, the first digit after the decimal is 2. - Bring down a zero.
Now, you divide 20 by 3.
20÷3=620 \div 3 = 620÷3=6 with a remainder of 2.
So, the next digit is 6. - Bring down another zero.
You get 20 again, and when you divide by 3, you get 6 with a remainder of 2 again.
This process will repeat infinitely.
Thus, the decimal representation of 83\frac{8}{3}38 is:2.6‾2.\overline{6}2.6
where the bar over the 6 indicates that it repeats indefinitely.
Why does this happen?
The reason the 6 repeats is due to the nature of division. When you divide 8 by 3, the remainder starts repeating after the first few steps, causing the same quotient (6) to appear over and over. This results in a repeating decimal.
Conclusion:
So, 83=2.6‾\frac{8}{3} = 2.\overline{6}38=2.6. This is an example of a repeating decimal, where the digit 6 repeats infinitely. In many cases, when dealing with repeating decimals, we use the bar notation to indicate the repeating portion, making it clear that the digit will continue without end.
