1/7 as decimal

Understand the Problem

The question is asking to convert the fraction 1/7 into its decimal representation. This involves dividing 1 by 7 to obtain a decimal value.

0.142857 (repeating)

The decimal representation of 1/7 is 0.142857 (repeating)

Steps to Solve

1. Set up the division problem

Since we want to find the decimal representation of $\frac{1}{7}$, we set up the long division of 1 divided by 7.

1. Perform the long division

Start the division. Since 7 cannot divide into 1, we add a decimal point and proceed to divide 10 (as 1.0).

1. Continue the division process
• 7 goes into 10 once (giving 0.1), with a remainder of 3.
• Bring down 0, making it 30. 7 goes into 30 four times (giving 0.14), with a remainder of 2.
• Bring down 0, making it 20. 7 goes into 20 twice (giving 0.142), with a remainder of 6.
• Continue this process until the pattern repeats.
1. Identify the repeating pattern

Continue the long division until the repeating decimal pattern becomes clear. In this case, the decimal value will repeat every 6 digits as 0.142857.

$$1 \div 7 = 0.142857142857...$$

The repeating cycle is "142857".

The decimal representation of 1/7 is 0.142857 (repeating)

The repeating cycle of the decimal value of $\frac{1}{7}$ is known as a repeating or recurring decimal. The pattern "142857" repeats indefinitely.