Quick Answer
1/5 as a decimal: 0.2
1/5 as a percent: 20%
One-fifth is a clean, easy-to-work-with fraction. Unlike 1/3 which produces a repeating decimal, 1/5 converts to a simple terminating decimal (0.2) and a round percentage (20%). This makes it one of the most convenient fractions for calculations.
How to Convert 1/5 to a Decimal
To turn a fraction into a decimal, divide the numerator (top number) by the denominator (bottom number).
Step-by-step:
1 ÷ 5 = ?
When you divide 1 by 5:
- 5 goes into 1 zero times, so we write 0.
- Add a decimal point and a zero: 1.0
- 5 goes into 10 exactly two times (5 × 2 = 10)
- No remainder - the division ends here!
1 ÷ 5 = 0.2
This is a terminating decimal - it ends cleanly after one decimal place. This happens because the denominator (5) has only 5 as a prime factor, and 5 is a factor of 10.
How to Convert 1/5 to a Percent
There are two common methods:
Method 1: From Decimal
Take the decimal (0.2) and multiply by 100:
0.2 × 100 = 20%
Method 2: Direct from Fraction
Multiply by 100 and divide by the denominator:
(1 × 100) ÷ 5 = 100 ÷ 5 = 20%
Both methods give the same result: 20%
Answer: 3 ÷ 5 = 0.6 = 60%
Reference Table: Fifth Fractions
| Fraction | Decimal | Percent | Common Use |
|---|---|---|---|
| 1/5 | 0.2 | 20% | One fifth of a whole |
| 2/5 | 0.4 | 40% | Two fifths |
| 3/5 | 0.6 | 60% | Three fifths |
| 4/5 | 0.8 | 80% | Four fifths |
Why Does 1/5 Terminate Cleanly?
Whether a fraction produces a terminating or repeating decimal depends on the denominator's prime factors:
- 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 5 is itself a prime factor of 5, and 5 is a factor of 10, the fraction 1/5 terminates after one decimal place.
Real-World Applications of 1/5
Grading:
If you get 1 out of 5 questions wrong, you scored 4/5 = 80%.
Star Ratings:
A 1-star rating out of 5 represents 20% satisfaction. A 5-star rating is 100%.
Tip Calculation:
A 20% tip (1/5 of the bill) is a common tipping amount. For a $50 meal: $50 × 0.2 = $10 tip.
Sales:
20% off means you pay 80% of the original price. For a $100 item: $100 × 0.8 = $80.
Equivalent Fractions to 1/5
You can create fractions equal to 1/5 by multiplying both the numerator and denominator by the same number:
- 1/5 = 2/10 (multiply by 2)
- 1/5 = 3/15 (multiply by 3)
- 1/5 = 4/20 (multiply by 4)
- 1/5 = 5/25 (multiply by 5)
- 1/5 = 20/100 (multiply by 20)
All these fractions convert to the same decimal: 0.2
Common Mistakes
- Confusing 1/5 with 1/4: 1/5 = 0.2 (20%), but 1/4 = 0.25 (25%). They're close but not the same.
- Writing 0.2% instead of 20%: Remember, 0.2 as a decimal equals 20% (multiply by 100), not 0.2%.
- Thinking 1/5 repeats: Unlike 1/3, 1/5 terminates cleanly at 0.2. No repeating pattern!
Quick Recap
1/5 is one of the easiest fractions to work with because:
- It converts to a clean decimal: 0.2
- It equals a round percentage: 20%
- It's commonly used for tips (20% tip is standard)
- It connects to the familiar 5-star rating system
For more fraction conversions, try our Fraction Calculator and Percentage Calculator.