# What is 4/9 as a decimal?

## Solution

A recurring decimal is a decimal in which a sequence of digits is repeated. A recurring or repeating decimal number is the result of long division where the division of the number gives the same remainders in the consecutive steps.

Some of the examples of recurring decimals are

0.4444…., 1.363636…., 0.48754875…., 0.7535353….

The digits that are repeated are indicated by placing a bar over the numbers.
The digits above can be written as

$$0.\overline4,\;1.\overline{36},\;0.\overline{4875},\;0.7\overline{53}$$

The long division method is used to convert the fractions to decimal forms. It can be observed that all the divisions do not give a decimal answer with remainder 0.

Some fractions give a decimal answer that has one or more digits repeating in a sequence and hence are called repeating or recurring decimals.

Let us take the example of a fraction $$\frac49$$ which will give us a simple recurring decimal number.

$$\hspace{4mm}0.44..\\9\overline{)4\color{Red}0}\\\frac{-36}{4\color{Red}0}\\\frac{-36}{4}$$

Here it can be seen that the number 4 is repeating in the steps of division and hence gives the same digits in the quotient.

Hence the answer is 0.4444…

As mentioned earlier, the recurring digits are written by placing a bar over the digit that is repeated.

Hence the decimal form of the fraction $$\frac49$$ is $$0.\overline4$$.

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac49$$, the number 4 is the dividend (our numerator)
• The number 9 is our divisor (our denominator)

Such a topic may be interesting for you: What is 15/16 as a decimal fraction?