Fraction to Decimal Converter: Master Conversions & Understand the Math
Recipe calls for 3/8 cup but your measuring cup shows decimals? Need to convert 0.625 to a fraction for homework? Let's demystify fraction-decimal conversions once and for all.
What You'll Learn
- Simple methods to convert fractions to decimals
- How to convert decimals back to fractions
- Understanding repeating vs terminating decimals
- Real-world applications in cooking, measurements, and more
- Common fractions you should memorize
Converting Fractions to Decimals
The secret to converting fractions to decimals? Divide the numerator by the denominator. That's it!
The Formula
a/b = a ÷ b
Numerator divided by Denominator
Example 1:
3/4 = 3 ÷ 4
= 0.75
Example 2:
1/8 = 1 ÷ 8
= 0.125
Example 3:
5/2 = 5 ÷ 2
= 2.5
Step-by-Step Example: Convert 5/8 to Decimal
Identify numerator (5) and denominator (8)
Divide numerator by denominator: 5 ÷ 8
Perform the division (use calculator if needed)
Result: 5/8 = 0.625
Converting Decimals to Fractions
Going the other way requires a few more steps, but it's still straightforward!
The 3-Step Method
Step 1: Write as a fraction over 1
Example: 0.75 becomes 0.75/1
Step 2: Multiply top and bottom by 10 for each decimal place
0.75 has 2 decimal places, so multiply by 100: (0.75 × 100)/(1 × 100) = 75/100
Step 3: Simplify the fraction
75/100 = 3/4 (divide both by 25)
More Examples
0.5 to fraction:
• 0.5/1 → 5/10 (multiply by 10) → 1/2 (simplify)
0.125 to fraction:
• 0.125/1 → 125/1000 (multiply by 1000) → 1/8 (divide by 125)
2.25 to fraction:
• 2.25/1 → 225/100 → 9/4 → 2 1/4 (as mixed number)
Understanding Repeating Decimals
Terminating Decimals
Decimals that end after a certain number of digits.
Rule: Terminating if denominator has only factors of 2 and/or 5
Repeating Decimals
Decimals where digits repeat infinitely (shown with a bar).
Rule: Repeating if denominator has factors other than 2 or 5
Converting Repeating Decimals to Fractions
Example: Convert 0.3̄ (0.333...) to a fraction
Let x = 0.333...
Multiply by 10: 10x = 3.333...
Subtract original: 10x - x = 3.333... - 0.333...
Simplify: 9x = 3
Solve: x = 3/9 = 1/3
Quick tip: For single repeating digit, put it over 9. For two digits, over 99. And so on!
Common Fractions You Should Memorize
Knowing these by heart saves time in cooking, tests, and everyday calculations:
Halves & Quarters
Thirds
Eighths
Fifths
Real-World Applications
Cooking & Baking
- Recipe scaling: Convert 2/3 cup to 0.67 for digital scales
- Portion control: 0.25 cup = 1/4 cup measuring spoon
- Ingredient ratios: 3/4 cup sugar = 0.75 cups
Measurements & DIY
- Woodworking: 5/16" = 0.3125 inches
- Drill bits: 0.375" = 3/8 inch bit
- Construction: 1/2" drywall = 0.5 inches thick
Finance & Business
- Stock prices: $45.75 = $45 and 3/4
- Interest rates: 6.25% = 6 1/4 percent
- Percentages: 0.15 = 15/100 = 15%
School & Testing
- Test scores: 17/20 = 0.85 = 85%
- GPA: 3.75 = 3 3/4 grade point average
- Probability: 1/4 chance = 0.25 = 25%
Common Mistakes to Avoid
Mistake #1: Dividing Denominator by Numerator
Wrong: 3/4 = 4 ÷ 3 = 1.333...
Right: 3/4 = 3 ÷ 4 = 0.75
Always divide TOP by BOTTOM!
Mistake #2: Forgetting to Simplify
Incomplete: 0.5 = 5/10
Complete: 0.5 = 5/10 = 1/2
Always reduce to lowest terms!
Mistake #3: Rounding Too Early
Problem: 1/3 ≈ 0.33, then 0.33 × 3 = 0.99 (not 1!)
Solution: Keep full precision or use the bar notation: 0.3̄
Round only at the end of calculations!
Convert Fractions & Decimals Instantly
Use our free fraction-decimal converter for quick, accurate conversions. Perfect for homework, cooking, and everyday calculations.
The Bottom Line
Converting between fractions and decimals isn't just a school exercise—it's a practical skill you'll use in cooking, construction, finance, and more. The basic method is simple: divide to get decimals, multiply and simplify to get fractions.
Master the common conversions (halves, quarters, eighths), understand when decimals repeat, and you'll handle any conversion with confidence. And when you need speed? Use our calculator—it's faster than doing long division by hand!