# What is 1/11 as a decimal?

## Want to practice?

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).

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