2/13 as a decimal
Understand the Problem
The question is asking us to convert the fraction 2/13 into its decimal form. This involves dividing the numerator (2) by the denominator (13).
Answer
The decimal form of $\frac{2}{13}$ is approximately $0.153846...$ (with 846 repeating).
Answer for screen readers
The decimal form of the fraction $\frac{2}{13}$ is approximately $0.153846$ (with 846 repeating).
Steps to Solve
- Set up the division
We need to divide the numerator by the denominator. This means we will calculate $2 \div 13$.
- Perform the division
Since 2 is smaller than 13, we will get 0 as the integer part. We will add a decimal point and zeros to continue the division. So we rewrite the problem as $2.000 \div 13$.
- Calculate the first decimal place
Now, we perform long division. 13 goes into 20 once.
The first digit after the decimal point is 0.1.
- Continue with the division
Now subtract $13 \times 1 = 13$ from 20, which gives us 7. Bring down the next zero, making it 70.
Next, 13 goes into 70 five times.
- Calculate the next decimal place
Now we calculate the next digit: the second decimal digit is 0.15, since $13 \times 5 = 65$.
- Continue with the division
Subtract again: $70 - 65 = 5$. Bring down the next zero to make it 50.
- Calculate the next decimal place again
13 goes into 50 three times. So, 0.153 is the new number: $13 \times 3 = 39$.
- Repeat until desired accuracy
Continue this process to get as many decimal places as needed. In total, the division gives us 0.153846 and repeats.
The decimal form of the fraction $\frac{2}{13}$ is approximately $0.153846$ (with 846 repeating).
More Information
The decimal representation of $\frac{2}{13}$ is a repeating decimal. This means that after a certain point, the digits will keep repeating indefinitely. The repeating part is "846".
Tips
One common mistake is stopping the division too early and not recognizing a repeating decimal. Make sure to continue the long division until you identify a repeating pattern.
