What is 4/13 as a decimal?
Understand the Problem
The question is asking for the decimal equivalent of the fraction 4/13. To find this, we will divide 4 by 13 using long division or a calculator.
Answer
$0.\overline{307692}$
Answer for screen readers
The decimal equivalent of the fraction $\frac{4}{13}$ is approximately $0.307692307692...$, which is a repeating decimal.
Steps to Solve
- Set up the long division
Begin by setting up the long division with 4 as the dividend and 13 as the divisor.
- Divide the first digit
Since 13 cannot go into 4, we will need to go to the next decimal place. We can think of 4 as 4.0 (or 40 tenths) by adding a decimal point and a zero.
- How many times does 13 fit into 40?
Now, calculate how many times 13 fits into 40.
13 fits into 40 two times (because $13 \times 2 = 26$).
- Subtract and bring down
Now, subtract 26 from 40 to get a remainder of 14. Then, bring down another 0, making it 140.
- Repeat the process
Now figure out how many times 13 fits into 140.
13 fits into 140 ten times (since $13 \times 10 = 130$).
- Subtract again and bring down
Subtract 130 from 140, leaving a remainder of 10. Bring down another 0 to get 100.
- Continue the division
Now determine how many times 13 fits into 100.
13 fits into 100 seven times (since $13 \times 7 = 91$).
- Final subtraction and more decimals
Subtract 91 from 100 to get 9. Bring down another 0 to get 90.
13 fits into 90 six times (since $13 \times 6 = 78$).
After several more iterations, we can continue this process to find more decimal places.
The decimal equivalent of the fraction $\frac{4}{13}$ is approximately $0.307692307692...$, which is a repeating decimal.
More Information
The fraction $\frac{4}{13}$ results in a repeating decimal that can go on indefinitely. The sequence "307692" repeats, which can be denoted as $0.\overline{307692}$. This fraction is also an example of a rational number that cannot be expressed as a finite decimal.
Tips
- Stopping Division Early: Many may stop after just a couple of steps, but repeating decimals need more iterations to understand the full context.
- Rounding Too Soon: Rounding the decimal too quickly can lead to loss of precision, especially important in further calculations.
