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).

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.

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