Write 7/11 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Understand the Problem
The question is asking to convert the fraction 7/11 into its decimal form, indicating any repeating digits if necessary.
Answer
$0.\overline{63}$
Answer for screen readers
The decimal representation of $\frac{7}{11}$ is $0.\overline{63}$.
Steps to Solve
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Set up the division To convert the fraction $\frac{7}{11}$ into decimal form, we need to perform long division of 7 by 11.
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Perform long division
- Divide 7 by 11. Since 7 is less than 11, we place a decimal point in the quotient and add a zero, making it 70.
- Next, 11 goes into 70 six times (since $11 \times 6 = 66$).
- Write 6 in the quotient and subtract 66 from 70, which gives us a remainder of 4.
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Continue the division
- Bring down another 0 (making it 40) and divide 40 by 11. This goes 3 times (since $11 \times 3 = 33$).
- Write 3 in the quotient and subtract 33 from 40, leaving a remainder of 7.
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Identify the repeating cycle
- Since we are back to the remainder of 7, this indicates a repeating cycle has begun. The digits '63' repeat.
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Express the final answer The decimal is represented as $0.\overline{63}$, with the bar indicating that '63' is the repeating part.
The decimal representation of $\frac{7}{11}$ is $0.\overline{63}$.
More Information
When a fraction results in a decimal with repeating digits, the bar notation is used to indicate which digits repeat. This is helpful for expressing irrational numbers and understanding their properties.
Tips
- Forgetting to place the decimal point and the leading zero when the dividend is less than the divisor.
- Miscalculating the multiplication for determining how many times the divisor fits into the current number.
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