## What is 1/3 in Decimal Form? One Third as a Decimal

*One third as a decimal is 0.333333… (with the 3s repeating infinitely). It is a recurring decimal because when you divide 1 by 3, you get a result with no remainder, but it continues infinitely without repeating the same sequence of digits, making it a non-terminating, repeating decimal.*

## Converting a Fraction to Decimal

Fractions represent numerical amounts in part-to-whole form. To understand or calculate with fractions more easily, we often convert them to decimal format. Converting a fraction to decimal involves dividing the numerator by the denominator.

Let’s convert the fraction 1/3 to its decimal equivalent.

## Understanding Fractions

A fraction expresses a relationship between two numbers:

- The numerator represents the number of parts we have
- The denominator is the total number of equal parts

So 1/3 indicates we have 1 out of 3 equal parts of a whole.

To visualize 1/3:

If we divide a whole into 3 equal slices, 1/3 represents having just 1 of those 3 equal slices.

## Decimal Division

To convert 1/3 to decimal:

1 / 3 = 0.3

Dividing the numerator 1 by the denominator 3 results in 0.3 recurring.

The 0.3 repeats infinitely without terminating. This makes 1/3 a recurring decimal.

## Recurring Decimals

1/3 = 0.333…

The 3 repeats endlessly because 3 cannot divide evenly into 1. The finite decimal representation of 1/3 is written with a bar over the recurring portion:

1/3 = 0.3̅

The bar indicates the 3 repeats indefinitely.

## Checking Our Work

We can convert 0.3̅ back to a fraction to verify it equals 1/3:

0.3̅ = 3/10 = 1/3 ✅

Since converting back gives us the original 1/3, this confirms that 0.3̅ is the correct decimal form.

Understanding fraction to decimal conversion provides a foundation for working with decimals as an extension of the rational number system.

In summary, to write a fraction as a decimal, divide the numerator by the denominator. Bar notation over recurring digits represents fractions that terminate infinitely.

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