# What is 3/11 as a decimal?

## Want to practice?

From the division above we can conclude that:

$$\frac{\mathbf3}{\mathbf{11}}\boldsymbol=\mathbf0$$.______

## Solution

1. Observe the long division to find the value of the divisor.
2. It can be seen that the result of the first step is 22 which is 2 times the divisor. From this, it can be deduced that the divisor is 11.
3. In the second step, the dividend value is 80. 11 divides 80 7 times to give 77. Hence the blank in the quotient should be 7.
4. Finally, the last blank is the remainder, which will be the result of 80-77 and is equal to 3.

Hence the completed division would be:

Note that the actual division starts from the decimal point, hence the dividend should be only 3 ( leaving out the 0).

Let us now write the fraction from the long division and its decimal form.

In a long division, the dividend is the numerator and the divisor is the denominator.
The fraction can be written as $$\frac3{11}$$.

The decimal form of the fraction is the quotient of the division, 0.27….. .

The decimal part is non-terminating because we get the same remainder in the 3rd step as in the first step. This shows that digits 2 and 7 are repeating digits.

The repeating digits are indicated by placing a bar over 2 and 7.

$$\frac3{11}=0.\overline{27}$$

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac3{11}$$, the number 3 is the dividend (our numerator)
• The number 11 is our divisor (our denominator)

Such a topic may be interesting for you: What is 3/10 as a decimal fraction?