What is 3/11 as a decimal?

3/11 as a decimal is 0.27272727...

Want to practice?

Question 1Convert the fraction

What is 3/11 written as a decimal?

Answer

0.27272727.

Divide 3 by 11.

Question 2Check with multiplication

How can you check the decimal value of 3/11?

Answer

Multiply 0.27272727 by 11; the result is 3.

Multiplication reverses the division used to convert the fraction.

Question 3Convert to a percentage

What percentage is equivalent to 3/11?

Answer

27.2727%.

Multiply the decimal 0.27272727 by 100.

Question 4Place the value on a number line

Between which two consecutive whole numbers does 3/11 lie?

Answer

It lies between 0 and 1.

Its decimal value is 0.27272727.

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?

Find More Fractions to Decimals

1/1 = 1	1/8 = 0.125	3/4 = 0.75	7/9 = 0.7	11/16 = 0.6875	8/9 = 0.8	7/8 = 0.875	4/5 = 0.8
1/2 = 0.5	1/9 = 0.1	2/5 = 0.4	3/10 = 0.3	15/32 = 0.4687	7/10 = 0.7	5/9 = 0.5	4/7 = 0.571
1/3 = 0.3	1/10 = 0.1	5/6 = 0.83	2/11 = 0.18	3/5 = 0.6	3/11 = 0.27	9/10 = 0.9
1/4 = 0.25	1/11 = 0.09	2/7 = 0.28571	5/11 = 0.45	3/7 = 0.428571	6/11 = 0.54	4/11 = 0.36
1/5 = 0.2	1/12 = 0.083	5/7 = 0.71428	8/11 = 0.72	6/7 = 0.85714	7/12 = 0.583	7/16 = 0.4375
1/6 = 0.16	1/16 = 0.0625	3/8 = 0.375	5/12 = 0.416	5/8 = 0.625	5/16 = 0.3125	15/16 = 0.9375
1/7 = 0.142857	2/3 = 0.6	2/9 = 0.2	3/16 = 0.1875	4/9 = 0.4	13/16 = 0.8125	19/32 = 0.5937