Write 11/3 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
The Correct Answer and Explanation is:
To convert the fraction ( \frac{11}{3} ) into a decimal, we divide 11 by 3. This is done through long division.
Long Division Process:
- Divide 11 by 3:
- 3 goes into 11 three times (since ( 3 \times 3 = 9 )), leaving a remainder of 2.
- Bring down a 0: Now we have 20 to divide.
- 3 goes into 20 six times (since ( 3 \times 6 = 18 )), leaving a remainder of 2 again.
- Bring down another 0: We have 20 once more.
- 3 goes into 20 six times again, with the same remainder of 2.
This process repeats indefinitely, with the digit 6 recurring. Thus, we express the decimal as ( 3.6666\ldots ), which is often written as ( 3.\overline{6} ), where the bar over the 6 indicates that it repeats infinitely.
Explanation:
- The division of 11 by 3 results in a non-terminating, repeating decimal. This means the decimal goes on forever without ending, but the digits start repeating at a certain point. In this case, the digit “6” keeps repeating.
- The repeating decimal is often written with a bar notation, such as ( 3.\overline{6} ), to indicate that the digit “6” repeats infinitely. This is a standard way of denoting repeating decimals, where the bar is placed over the digits that repeat.
- To verify the result, you can multiply ( 3.\overline{6} ) by 3:
- ( 3.\overline{6} \times 3 = 11 ). This confirms that the decimal is correct.
Therefore, ( \frac{11}{3} ) as a decimal is ( 3.\overline{6} ), where the 6 repeats indefinitely. This is the correct and precise representation of the fraction in decimal form.