What is 1/11 as a decimal?

1/11 as a decimal is 0.09

Want to practice?

Question 1Convert the fraction

What is 1/11 written as a decimal?

Answer

0.09090909.

Divide 1 by 11.

Question 2Check with multiplication

How can you check the decimal value of 1/11?

Answer

Multiply 0.09090909 by 11; the result is 1.

Multiplication reverses the division used to convert the fraction.

Question 3Convert to a percentage

What percentage is equivalent to 1/11?

Answer

9.0909%.

Multiply the decimal 0.09090909 by 100.

Question 4Place the value on a number line

Between which two consecutive whole numbers does 1/11 lie?

Answer

It lies between 0 and 1.

Its decimal value is 0.09090909.

Complete the given division and fill in the blanks.

Solution

Step 1:

Add a decimal point to the quotient as 11 > 1 and is not divisible. By doing so we can add one 0 to the dividend to make it 10. As it can be noted that 10 is still less than 11, add another 0 to the quotient and to the dividend to make it 100.

Step 2:

Continue division until the remainder is repeated. Here we can see that the remainder 1 is repeated after two steps. Hence the answer is a non-terminating decimal number.

A non-terminating decimal number is a number in which one digit or a sequence of digits are repeated continuously.

To denote these values in a terminating form, we write the numbers that are repeated with a bar over them.

Here the quotient is 0.0909…… and can be written as

$$1\div11=0.\overline{09}$$

$$\frac1{11}=0.\overline{09}$$

The division of the numerator by the denominator gives the decimal form of the fraction.

Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac1{11}$$, the number 1 is the dividend (our numerator)
• The number 11 is our divisor (our denominator).

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

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