What is 3/13?

Understand the Problem

The question is asking for the fraction 3/13 to be expressed in decimal form or simplified if possible.

Answer

$0.\overline{230769}$

Steps to Solve

Convert the Fraction to Decimal To convert the fraction $\frac{3}{13}$ into decimal form, we perform the division of the numerator by the denominator.

So we calculate:

$$ 3 \div 13 $$

Perform Long Division We can set up long division or use a calculator to divide.

Performing long division:

3 goes into 13 zero times (0).
Add a decimal point and a zero to make it 30.
13 goes into 30 two times (2): $2 \times 13 = 26$.
Subtract 26 from 30, which leaves you with 4.
Bring down another zero to make it 40.
13 goes into 40 three times (3): $3 \times 13 = 39$.
Subtract 39 from 40, which leaves you with 1.
Bring down another zero to make it 10.
13 goes into 10 zero times (0).
Bring down the next zero for 100, and so on.

Continuing this process, we find:

$$ 3 \div 13 = 0.230769230769... $$

Recognize the Repeating Decimal The decimal can be noted as $0.\overline{230769}$ indicating that the sequence "230769" repeats.

The decimal form of $\frac{3}{13}$ is $0.\overline{230769}$.

More Information

The fraction $\frac{3}{13}$ results in a repeating decimal, which means that the digits "230769" will continue indefinitely. This type of decimal is common in fractions where the denominator does not have factors of 2 or 5.

Tips

A common mistake is truncating the decimal too early and not recognizing it as a repeating decimal.
Another mistake can occur by not performing proper long division, leading to incorrect results.

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