# What is 1/3 as a decimal?

## Want to practice?

Gary ate one piece of his cake that was cut in three. How can he write the quantity of cake he had as a decimal?

## Solution

The way of representing a part of something is called fractions. Fraction helps to denote the values that are not whole numbers.

Example: One part out of two or ‘half’ is represented as $$\frac12$$.

Similarly, all values that are not whole numbers can be represented as fractions. Fractions can also be used to represent whole numbers.

Here the fraction for ‘one piece out of three’ is represented as ‘one out of 3’ or $$\frac13$$.

Fractions can also be written in decimal form using the decimal point to separate the whole numbers and the partial numbers.

The long division method is used to convert fractions to decimals by dividing the numerator by the denominator.

It can be seen that the quotient is started with a decimal point (0.) so that we can add 0 to 1 to make it divisible by 3.

The division gives the same remainder 1 in each step of division, hence the answer has the digit 3 repeating infinitely.

The answer can be written as 0.33… or as  $$\mathbf0\boldsymbol.\overset{\boldsymbol¯}{\mathbf3}$$.

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac13$$, the number 1 is the dividend (our numerator)
• The number 3 is our divisor (our denominator)

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