1/3 as a Percent and Decimal - Complete Step-by-Step Guide #1

Quick Answer

1/3 as a decimal: 0.333... (repeating)

1/3 as a percent: 33.33% (approximately)

The three dots after 0.333 mean the 3s continue forever. This is called a repeating decimal or recurring decimal. Unlike fractions like 1/2 (which equals exactly 0.5), one-third goes on forever.

Key Takeaway: 1/3 cannot be written as an exact decimal because it produces an infinite repeating pattern. For practical purposes, we often round it to 0.33 or 0.333.

How to Convert 1/3 to a Decimal

To turn a fraction into a decimal, divide the numerator (top number) by the denominator (bottom number).

Step-by-step:

1 ÷ 3 = ?

When you divide 1 by 3:

3 goes into 1 zero times, so we write 0.
Add a decimal point and a zero: 1.0
3 goes into 10 three times (3 × 3 = 9), remainder 1
Add another zero: 10
3 goes into 10 three times again, remainder 1
This pattern repeats forever!

1 ÷ 3 = 0.333333...

We can write this with a bar over the repeating digit: 0.3̄

How to Convert 1/3 to a Percent

There are two ways to do this:

Method 1: From Decimal

Take the decimal (0.333...) and multiply by 100:

0.333... × 100 = 33.333...%

Method 2: Direct from Fraction

Multiply by 100 and divide by the denominator:

(1 × 100) ÷ 3 = 100 ÷ 3 = 33.333...%

For most practical purposes, we round this to 33.33% or 33 1/3%.

Try It: What is 2/3 as a decimal and percent?

Answer: 2 ÷ 3 = 0.666... = 66.67%

Reference Table: Common Third Fractions

Fraction	Decimal	Percent	Common Use
1/3	0.333...	33.33%	One third of a whole
2/3	0.666...	66.67%	Two thirds of a whole
1/6	0.1666...	16.67%	Half of 1/3
1/9	0.111...	11.11%	One ninth (⅓ of ⅓)

Why Does 1/3 Repeat Forever?

Not all fractions produce repeating decimals. Whether a fraction repeats depends on the denominator:

Terminating decimals: Denominators with only 2s and 5s as prime factors (like 1/2, 1/4, 1/5, 1/8, 1/10)
Repeating decimals: Any other prime factors (like 1/3, 1/6, 1/7, 1/9)

Since 3 cannot be made from 2s and 5s, 1/3 produces a repeating decimal.

Working with 1/3 in Calculations

When to use the fraction form (1/3):

When you need exact answers
In algebra and higher math
When multiplying with other fractions

When to use decimal (0.333):

In everyday calculations
When using a calculator
When comparing values

Real-World Example:

You want to split a $60 restaurant bill among 3 people. Each person pays:

$60 × 1/3 = $60 × 0.333... = $20

In this case, it divides evenly! That's because 60 is divisible by 3.

Equivalent Fractions to 1/3

You can create fractions equal to 1/3 by multiplying both the top and bottom by the same number:

1/3 = 2/6 (multiply by 2)
1/3 = 3/9 (multiply by 3)
1/3 = 4/12 (multiply by 4)
1/3 = 5/15 (multiply by 5)

All these fractions convert to the same decimal: 0.333...

Common Mistakes

Rounding too early: If you round 0.333 to 0.33 and then multiply large numbers, your final answer may be wrong.
Forgetting the bar notation: In math class, write 0.3̄ (with a bar) to show it repeats.
Confusing 33.33% with 33%: 1/3 is closer to 33.33% than to 33%. Use enough decimal places for precision.

Quick Recap

1/3 is a special fraction because:

It produces a repeating decimal (0.333...)
It equals approximately 33.33%
When possible, keep it as fraction form for exact calculations
It represents one part when something is divided into three equal parts

Remember: When you see a fraction with 3 in the denominator, expect a repeating decimal. The more you work with these, the more natural they become.

For more fraction conversions, try our Fraction Calculator and Percentage Calculator.