What is 4/13 as a decimal?
Understand the Problem
The question is asking to convert the fraction 4/13 into a decimal form. This involves dividing the numerator (4) by the denominator (13) to obtain the decimal representation.
Answer
0.3077
Answer for screen readers
The decimal form of $ \frac{4}{13} $ is approximately 0.3077.
Steps to Solve
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Set up the division To convert the fraction $ \frac{4}{13} $ into decimal form, we will divide 4 by 13.
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Perform the division Using long division, divide 4 by 13. Since 4 is less than 13, we can add a decimal and zeros to continue division.
- We write 4.000 (the decimal point is added).
- Now, we perform the division: 13 goes into 40 three times.
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Calculate and subtract Calculate $ 3 \times 13 = 39 $. Then subtract this from 40. $$ 40 - 39 = 1 $$
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Bring down the next digit Bring down the next 0, making it 10. Now, divide 10 by 13.
- 13 goes into 10 zero times.
- Continuing the division Add another 0 to make it 100. Now, divide 100 by 13.
- 13 goes into 100 seven times.
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Calculate and repeat Calculate $ 7 \times 13 = 91 $. Subtract to find the remainder. $$ 100 - 91 = 9 $$
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Bring down another digit Bring down another 0, making it 90, and repeat the process.
- 13 goes into 90 six times.
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Final calculations Calculate $ 6 \times 13 = 78 $. Then subtract. $$ 90 - 78 = 12 $$
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Continue repeating until satisfied Keep bringing down zeros, following the same process, resulting in $ 4/13 \approx 0.307692307...$ or rounded to $ 0.308 $.
The decimal form of $ \frac{4}{13} $ is approximately 0.3077.
More Information
$ \frac{4}{13} $ is a repeating decimal, which means that it continues indefinitely. The decimal representation typically rounds to 0.3077 for convenience.
Tips
- Not adding a decimal and zeros when the numerator is less than the denominator.
- Stopping the division too early without recognizing the decimal continues.
