Decimal Fraction Conversion
Closest fractional approximation
Required Parameters
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Quick Answer
Convert decimals to fractions by multiplying by the desired denominator. 0.375 = 3/8 (multiply by 8, get 3). Common equivalents: 1/4 = 0.25, 1/3 = 0.333, 1/2 = 0.5, 3/4 = 0.75. Essential for drill sizes, machining, and Imperial measurements.
Decimal to Fraction Converter
Convert decimal numbers to fractions and vice versa. Useful for measurements and precision calculations.
Examples
- 0.5 = 1/2
- 0.25 = 1/4
- 0.125 = 1/8
- 0.333... = 1/3
Design Notes
Fractional inches are standard in US manufacturing: drill bit sizes, wrench sizes, pipe fittings, and lumber dimensions all use fractions. PCB mounting holes typically use fractional inch drills (1/8 inch, 5/32 inch). The continued fraction algorithm finds the best rational approximation.
Common Mistakes
- 1
Confusing decimal inches with fractional inches — 0.125 inch = 1/8 inch, not approximately 1/8.
- 2
Using fractions for metric measurements — metric uses decimals (2.5 mm, not 2 1/2 mm).
- 3
Forgetting to reduce fractions to lowest terms after conversion.
Knowledge Base
Why use fractions instead of decimals?
Fractions are essential in manufacturing: drill bit sizes (1/16, 5/64, 3/32 inch), wrench sizes (7/16, 9/16, 11/16), pipe fittings (1/4, 3/8, 1/2 inch), and lumber dimensions (3/4 inch plywood). Machine shop measurements are in fractional inches (1/16th or 1/32nd inch precision).
How do I convert a decimal to a fraction?
Method: multiply by the desired denominator. For 1/16 precision: 0.375 × 16 = 6, so 0.375 = 6/16 = 3/8. For 1/32 precision: 0.375 × 32 = 12, so 0.375 = 12/32 = 3/8. If the result is not a whole number, round to nearest and note the approximation error.
What are common fraction-decimal equivalents?
1/4 = 0.250, 1/3 = 0.333, 3/8 = 0.375, 1/2 = 0.500, 5/8 = 0.625, 2/3 = 0.667, 3/4 = 0.750, 7/8 = 0.875. For sixteenths: 1/16 = 0.0625, 3/16 = 0.1875, 5/16 = 0.3125, 7/16 = 0.4375, 9/16 = 0.5625.
What is a repeating decimal?
Some fractions produce infinite repeating decimals: 1/3 = 0.333..., 1/6 = 0.1666..., 1/7 = 0.142857142857..., 1/9 = 0.111..., 1/11 = 0.090909.... Any fraction with a denominator that has prime factors other than 2 or 5 produces a repeating decimal.
How are fractions used in electronics?
Fractional inches for: PCB mounting holes (typically 1/8 or 5/32 inch), connector pin spacing (0.1 inch = 100 mil), standoff heights (1/4, 3/8, 1/2 inch), and wire gauges (some tables use fractional inch diameters). Metric is increasingly preferred but Imperial fractions persist in US manufacturing.
What is the continued fraction method?
The most efficient algorithm for finding the best rational approximation. It works by repeatedly taking the integer part and reciprocal of the remainder. Example: π = 3 + 1/(7 + 1/(15 + 1/(1 + ...))) giving approximations 3, 22/7, 333/106, 355/113. 355/113 is accurate to 7 decimal places.
How do I simplify a fraction?
Divide both numerator and denominator by their Greatest Common Divisor (GCD). Example: 12/16 — GCD(12,16) = 4, so 12/16 = 3/4. Finding GCD: use the Euclidean algorithm (repeated division) or factor both numbers. 12 = 2²×3, 16 = 2⁴, GCD = 2² = 4.
What is a mixed number?
A whole number plus a fraction: 3 1/2 = 3.5, 2 3/4 = 2.75. To convert mixed to improper fraction: multiply whole by denominator, add numerator. 3 1/2 = (3×2+1)/2 = 7/2. Reverse: divide numerator by denominator. 7/2 = 3 remainder 1 = 3 1/2.
What fraction precision do machinists use?
Typical machine shop precision: 1/64 inch (0.015625 inch = 0.397 mm) for general work. CNC machining: 0.001 inch (1 mil) or better, usually specified as decimals. Drill bits come in fractional (1/64 to 1 inch), wire number (#1-#80), letter (A-Z), and metric (0.5mm-25mm) sizes.
How does IEEE 754 floating-point relate to fractions?
Computers store decimals as binary fractions: 0.5 = 1/2 (exact), 0.25 = 1/4 (exact), but 0.1 = a repeating binary fraction (cannot be stored exactly). This is why 0.1 + 0.2 = 0.30000000000000004 in JavaScript. For exact decimal arithmetic, use integer math with scaling or libraries like BigDecimal.