Decimal to Fraction Calculator
Convert terminating and repeating decimals into reduced fractions, mixed numbers, and inch fractions with full GCF reduction steps.
Decimal Input
Fractional Results
Step 2: Greatest Common Factor (GCF) of 375 and 1000 is 125
Step 3: 375 ÷ 125 = 3, 1000 ÷ 125 = 8
Final Simplified Fraction: 3 / 8
Converting Decimals to Fractions in Real Life
Whether you are reading a carpenter's tape measure, adjusting recipe ingredients in culinary arts, or converting CNC machining coordinates into drill bit fractional sizes, translating floating-point decimals to simplified rational numbers is an essential mathematical skill.
For related problem solving and complete calculations, you can also explore our Fraction Calculator and Percentage Calculator.
Common Inch Fraction Equivalents
- 0.125: 1/8 inch
- 0.250: 1/4 inch
- 0.375: 3/8 inch
- 0.500: 1/2 inch
- 0.625: 5/8 inch
- 0.750: 3/4 inch
- 0.875: 7/8 inch
Frequently Asked Questions
How do you convert a terminating decimal to a fraction?
1) Write down the decimal divided by 1 (e.g., 0.375 / 1). 2) Multiply both numerator and denominator by 10 for every digit after the decimal point (0.375 × 1000 / 1000 = 375 / 1000). 3) Find the Greatest Common Factor (GCF) of both numbers (GCF of 375 and 1000 is 125). 4) Divide both by the GCF: 375 ÷ 125 = 3 and 1000 ÷ 125 = 8, yielding 3/8.
How do you convert repeating decimals (like 0.333... or 0.1666...) to a fraction?
Using algebra: Let x = 0.1666... Multiply by 100: 100x = 16.666... Multiply by 10: 10x = 1.666... Subtract the two equations: 100x - 10x = 16.666... - 1.666..., which gives 90x = 15. Solving for x: x = 15/90, which simplifies to 1/6.
What is the difference between a proper fraction and an improper fraction?
A proper fraction has a numerator smaller than its denominator (e.g., 3/8), representing a value strictly less than 1. An improper fraction has a numerator greater than or equal to its denominator (e.g., 21/8), which can also be expressed as a mixed number (2 5/8).
What if my decimal is negative?
A negative decimal converts to a negative fraction with the same absolute numerical relationship. For example, -0.75 converts directly to -3/4.
Can every decimal be converted to a fraction?
No. Only rational numbers (terminating decimals and repeating periodic decimals) can be represented as the ratio of two integers (a / b). Irrational numbers like π (3.14159...) or √2 (1.41421...) have infinite non-repeating decimal expansions and cannot be written as exact fractions.