Answer: The fraction 6/7 is a non-terminating recurring decimal
Explanation:
To determine if the fraction 6/7 is a non-terminating recurring decimal, we can perform the division step by step. Here's the process:
Step 1: Divide 6 by 7:
- The quotient is 0, and the remainder is 6.
Step 2: Multiply the remainder by 10 and divide by 7:
- Multiply 6 by 10, resulting in 60.
- Divide 60 by 7:
- The quotient is 8, and the remainder is 4.
Step 3: Repeat Step 2 until we obtain a recurring pattern or the remainder becomes 0.
Step 2 (repeated): Multiply the remainder (4) by 10 and divide by 7:
- Multiply 4 by 10, resulting in 40.
- Divide 40 by 7:
- The quotient is 5, and the remainder is 5.
Step 2 (repeated): Multiply the remainder (5) by 10 and divide by 7:
- Multiply 5 by 10, resulting in 50.
- Divide 50 by 7:
- The quotient is 7, and the remainder is 1.
Step 2 (repeated): Multiply the remainder (1) by 10 and divide by 7:
- Multiply 1 by 10, resulting in 10.
- Divide 10 by 7:
- The quotient is 1, and the remainder is 3.
Step 2 (repeated): Multiply the remainder (3) by 10 and divide by 7:
- Multiply 3 by 10, resulting in 30.
- Divide 30 by 7:
- The quotient is 4, and the remainder is 2.
Step 2 (repeated): Multiply the remainder (2) by 10 and divide by 7:
- Multiply 2 by 10, resulting in 20.
- Divide 20 by 7:
- The quotient is 2, and the remainder is 6.
Step 2 (repeated): Multiply the remainder (6) by 10 and divide by 7:
- Multiply 6 by 10, resulting in 60.
- Divide 60 by 7:
- The quotient is 8, and the remainder is 4.
Step 3 (repeated): Since we have encountered the same remainder (4) again, we can conclude that the division will continue with the same pattern indefinitely.
Therefore, the fraction 6/7 is a non-terminating recurring decimal. In decimal form, it can be represented as 0.857142857142857..., with the sequence "857142" repeating indefinitely.