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.
Answer
0.142857 (repeating)
Answer for screen readers
The decimal representation of 1/7 is 0.142857 (repeating)
Steps to Solve
- 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.
- 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).
- 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.
- 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)
More Information
The repeating cycle of the decimal value of $\frac{1}{7}$ is known as a repeating or recurring decimal. The pattern "142857" repeats indefinitely.
Tips
Common mistakes include stopping the long division too early before identifying the repeating pattern, or incorrectly performing the division steps. Always ensure accuracy by continuing the division until you spot the repetition.
