9/13 as a decimal
Understand the Problem
The question is asking for the decimal representation of the fraction 9/13. This can be found by performing the division of 9 by 13.
Answer
The decimal representation of the fraction $\frac{9}{13}$ is $0.\overline{692307}$.
Answer for screen readers
The decimal representation of the fraction $\frac{9}{13}$ is approximately $0.692307...$, which can be expressed as $0.\overline{692307}$.
Steps to Solve
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Set Up the Division Begin by setting up the long division of 9 by 13.
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Perform the Division Since 9 is less than 13, the integer part of the division is 0. Now, we add a decimal point and zeros to 9, changing it to 9.000...
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Divide the First Digit Now divide 13 into 90 (the first two digits after the decimal).
- 13 goes into 90 a total of 6 times (because $13 \times 6 = 78$).
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Subtract and Bring Down Subtract 78 from 90, which gives: $$ 90 - 78 = 12 $$ Now bring down the next zero to make it 120.
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Continue the Division Now divide 13 into 120.
- It goes in 9 times ($13 \times 9 = 117$).
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Subtract Again Subtract 117 from 120: $$ 120 - 117 = 3 $$ Bring down another zero to make it 30.
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Final Division Steps Divide 13 into 30:
- It goes in 2 times ($13 \times 2 = 26$). Then, subtract: $$ 30 - 26 = 4 $$ Bring down another zero to make it 40.
Repeat this process:
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13 goes into 40 a total of 3 times ($13 \times 3 = 39$).
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Subtract to get: $$ 40 - 39 = 1 $$ Bring down 0 to get 10.
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Divide again: 13 into 10 goes 0 times.
This process continues indefinitely.
- Identify the Pattern After repeating the division, you’ll notice that the decimal representation of $9/13$ starts to show a pattern: $0.692307692307...$ with "692307" repeating.
The decimal representation of the fraction $\frac{9}{13}$ is approximately $0.692307...$, which can be expressed as $0.\overline{692307}$.
More Information
The fraction $\frac{9}{13}$ is a repeating decimal. This means that it does not end but goes on forever in a repeating sequence. Repeating decimals often occur from fractions that can't be simplified into finite decimal numbers.
Tips
- Forgetting to add the decimal point and zeros when dividing a smaller numerator by a larger denominator.
- Miscalculating the multiplication or subtraction steps leading to incorrect remainders.
- Not recognizing the repeating pattern in the decimal.
