Decimal to Fraction Calculator
Convert any decimal to a simplified fraction — terminating (0.75 → 3/4) or repeating (0.333... → 1/3). Also simplifies fractions, compares them, and performs arithmetic with step-by-step solutions.
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How It Works
Count the decimal places (n). Write as decimal_part / 10^n. Simplify by dividing both by GCF. For 0.375: 375/1000. GCF(375,1000)=125. 375÷125=3, 1000÷125=8. Result: 3/8. The denominator of a terminating decimal fraction (in lowest terms) only contains factors 2 and 5.
0.d₁d₂...dₙ = d₁d₂...dₙ / 10^n, then ÷ GCF0.75 = 75/100 = 3/4 | 0.125 = 125/1000 = 1/8Algebraic method: let x = 0.333..., multiply by 10 (or 100 for two-digit repeating block), subtract the original equation to eliminate the repeating part, solve for x, simplify. 0.272727...: let x=0.272727..., 100x=27.272727..., 99x=27, x=27/99=3/11.
x = 0.R̄ → 10^k × x = R + x → x = R/(10^k − 1)0.333... = 1/3 | 0.2727... = 27/99 = 3/11Switch to the Simplify tab. Enter numerator and denominator. The calculator divides both by GCF to get the fully reduced fraction. Also shows: decimal equivalent, percentage, and whether the fraction is proper (n<d), improper (n>d), or a whole number. For 48/72: GCF=24, simplified=2/3.
Simplified = (n/GCF)/(d/GCF) where GCF = GCF(n,d)48/72: GCF=24 → 2/3 | 18/6: GCF=6 → 3 (whole)Switch to the Compare tab. Enter two fractions. The calculator converts both to a common denominator (LCD) and compares. Shows the relationship (a/b > c/d, < or =) and the decimal values of both fractions for easy comparison. Also shows the difference between them.
Compare a/b vs c/d: convert to LCD, compare numerators3/4 vs 7/10: LCD=20 → 15/20 vs 14/20 → 3/4 > 7/10Switch to Operations. Enter two fractions and select +, −, ×, or ÷. Full step-by-step solution displays: finding LCD for addition/subtraction, multiplying numerators for multiplication, or flipping for division. Result in simplified form and as a mixed number. Example: 3/4 + 1/6 = 9/12 + 2/12 = 11/12.
Add: LCD method | Multiply: (a/b)×(c/d) = ac/bd | Divide: flip & multiply3/4 + 1/6 = 11/12 | 2/3 × 3/4 = 1/2 | 1/2 ÷ 3/4 = 2/3Quick Reference
Common decimal-to-fraction conversions.
Convert
0.5
1/2
Convert
0.75
3/4
Convert
0.125
1/8
Convert
0.625
5/8
Repeating
0.333...
1/3
Repeating
0.666...
2/3
Repeating
0.142857...
1/7
Repeating
0.272727...
3/11
Tips & Shortcuts
The Decimal → Fraction tab opens by default. Enter any decimal — the calculator auto-detects terminating vs repeating and applies the correct conversion method.
For repeating decimals, enter the repeating portion as many times as needed (e.g. 0.142857142857 for 1/7) — the calculator identifies the pattern.
After converting, check the decimal equivalent in the result to verify: 5/8 should show 0.625. If it matches your input, the conversion is correct.
Use the Compare tab to verify that two fractions are equivalent: 3/4 and 75/100 should show = (equal). If not equal, one is incorrect.
Mixed numbers display automatically for improper fractions: 11/4 shows as 2¾. This helps when working with measurements or recipes.
Common Mistakes
Converting 0.1 + 0.2 and expecting 0.3 exactly
0.1+0.2 = 0.30000000000000004 in floating-point — a binary representation issue. As fractions: 1/10 + 1/5 = 1/10 + 2/10 = 3/10 = 0.3 exactly. Use fraction arithmetic for exact results.
Writing 0.333 and expecting 1/3
0.333 (terminating, 3 decimal places) = 333/1000, which does not simplify to 1/3. The repeating decimal 0.333... (infinite 3s) = 1/3. Enter enough repeating digits for the calculator to detect the pattern, or enter 0.3333333333 for a close approximation.
Expecting π or √2 to convert to a fraction
Irrational numbers have no exact fraction form. π ≈ 355/113 (accurate to 6 decimal places) and √2 ≈ 1414/1000 = 707/500 are approximations, not exact. The calculator converts the decimal approximation, not the true irrational value.
Not simplifying the result further
The calculator always returns the fully simplified fraction (GCF applied). If you computed manually and got 6/8, simplify by GCF(6,8)=2 to get 3/4. Enter 6/8 in Simplify mode to confirm.
Confusing the decimal as percentage when reading result
The result panel shows both fraction form and decimal. 3/4 = 0.75 = 75%. These are three representations of the same value — do not confuse the decimal 0.75 with the percentage 75%.
Frequently Asked Questions
Count the decimal places (n). Write as decimal_digits / 10^n. Then divide both by their GCF. For 0.75: 75/100, GCF(75,100)=25, → 3/4. For 0.125: 125/1000, GCF=125, → 1/8. For 0.6: 6/10, GCF=2, → 3/5. The calculator does all steps instantly.
0.333... = 1/3 exactly. Algebraic proof: let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, x = 3/9 = 1/3. Similarly: 0.666... = 2/3, 0.111... = 1/9, 0.142857142857... = 1/7. Enter the repeating decimal directly and the calculator converts it.
0.5 = 5/10 = 1/2. GCF(5,10)=5, so divide both: 5÷5=1, 10÷5=2. Result: 1/2. The denominator 10 factors as 2×5. Since the only prime factors are 2 and 5, 0.5 is a terminating decimal — exactly representable as a fraction.
0.625 = 625/1000. GCF(625,1000): 625=5⁴, 1000=2³×5³. GCF=5³=125. 625÷125=5, 1000÷125=8. Simplified: 5/8. Verify: 5÷8=0.625 ✓. The fraction 5/8 is in lowest terms because GCF(5,8)=1.
Terminating: a finite number of digits (0.25, 0.5, 0.125). Convert by placing over 10^n and simplifying. They always come from fractions whose denominator (in lowest terms) has only factors 2 and 5. Repeating: infinitely repeating pattern (0.333..., 0.142857...). Use the algebraic method. Fractions with other prime factors (3, 7, 11...) in the denominator always give repeating decimals.
0.1 = 1/10. GCF(1,10)=1 so it is already in lowest terms. Notable: 0.1 cannot be represented exactly in binary floating-point (computers store it as approximately 0.1000000000000000055...). This is why 0.1+0.2 ≠ 0.3 in many programming languages. But as a fraction, 1/10 is exact.
Only rational numbers (terminating or repeating decimals) convert to exact fractions. Irrational numbers like π=3.14159265..., √2=1.41421356..., and e=2.71828... are non-repeating and non-terminating — they have no fraction representation. Any decimal that terminates OR has a repeating block is rational and converts exactly.
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