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Is 6/7 a non terminating recurring decimal​

2 Answers

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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.

User Liyansong
by
7.5k points
6 votes

Answer: yes

Explanation:

6/7 in decimal notation has unlimited decimal places. That is, 6/7 as decimal is a non-terminating, repeating decimal.

User Vrushank
by
8.4k points