Converting Between Percentages, Decimals, and Fractions

Why Learn These Conversions?

Percentages, decimals, and fractions are three different ways of expressing the same value. Being able to convert between them quickly is a fundamental math skill used in everyday life, from calculating tips and discounts to understanding statistics and financial reports. Once you understand the relationships, conversions become second nature.

The Core Relationships

Converting Percentages to Decimals

Divide the percentage by 100 (or move the decimal point two places to the left):

• 75% = 75 ÷ 100 = 0.75
• 8% = 8 ÷ 100 = 0.08
• 125% = 125 ÷ 100 = 1.25
• 0.5% = 0.5 ÷ 100 = 0.005

Converting Decimals to Percentages

Multiply the decimal by 100 (or move the decimal point two places to the right):

• 0.45 = 0.45 × 100 = 45%
• 0.07 = 0.07 × 100 = 7%
• 1.5 = 1.5 × 100 = 150%
• 0.003 = 0.003 × 100 = 0.3%

Converting Fractions to Percentages

Divide the numerator by the denominator, then multiply by 100:

• 3/4 = (3 ÷ 4) × 100 = 0.75 × 100 = 75%
• 1/3 = (1 ÷ 3) × 100 = 0.3333 × 100 = 33.33%
• 5/8 = (5 ÷ 8) × 100 = 0.625 × 100 = 62.5%

Converting Percentages to Fractions

Place the percentage over 100 and simplify:

• 25% = 25/100 = 1/4
• 60% = 60/100 = 3/5
• 37.5% = 37.5/100 = 375/1000 = 3/8

Common Equivalents Reference Table

Converting Decimals to Fractions

Step-by-Step Method

1. Write the decimal as a fraction over a power of 10 based on decimal places.
2. Simplify by dividing both numerator and denominator by their greatest common factor (GCF).

Example: Convert 0.35 to a fraction:

1. 0.35 = 35/100
2. GCF of 35 and 100 is 5
3. 35 ÷ 5 = 7, 100 ÷ 5 = 20
4. Answer: 7/20

Repeating Decimals

For repeating decimals like 0.333..., recognize common patterns:

• 0.333... = 1/3
• 0.666... = 2/3
• 0.1666... = 1/6
• 0.1428571... = 1/7
• 0.0909... = 1/11

Quick Conversion Tips

• Memorize common equivalents: Knowing that 1/4 = 25%, 1/3 ≈ 33.3%, and 1/5 = 20% makes mental math much faster.
• For percentages to decimals: Just move the decimal point two places left. No calculator needed.
• For fractions to percentages: If the denominator is a factor of 100 (like 4, 5, 10, 20, 25, 50), conversion is easy by finding an equivalent fraction with 100 as the denominator.
• Check your work: Convert back using the reverse method to verify your answer.
• Practice with everyday items: When you see a sale for "1/3 off," instantly know that is about 33.3% off.

Practice Problems