Decimal to Fraction
Convert Terminating or Repeating Decimals into Simplified Fractions.
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How to Convert Decimals to Fractions Manually
While this calculator provides instant precision, understanding the mechanics behind the conversion is essential for students, engineers, and tradespeople. Converting a decimal value into a fraction involves different methods depending on whether the decimal terminates (ends) or repeats infinitely.
1. Converting Terminating Decimals
A terminating decimal is a number that has a finite number of digits after the decimal point (e.g., 0.75 or 3.142). The logic here relies on “Place Value.”
The Step-by-Step Method:
- Identify the Place Value: Count the number of digits to the right of the decimal point. Let’s call this number n.
- Create the Fraction: The numerator is the decimal number without the dot. The denominator is 10 raised to the power of n (1 followed by n zeros).
- Simplify: Reduce the fraction by dividing both the top and bottom by their Greatest Common Divisor (GCD).
There are 3 digits after the decimal, so we divide by 1000 (103).
Both numbers are divisible by 125 (the GCD):
2. Converting Repeating Decimals
Repeating decimals (like 0.333… or 1.66…) require an algebraic approach because you cannot simply write them over a power of 10.
The “Subtraction” Method: To remove the infinite repeating part, we create two algebraic equations and subtract them.
- Step A: Let x equal the decimal number.
- Step B: Create Equation 1 by multiplying x by a power of 10 that moves the decimal point to the right of the repeating digits.
- Step C: Create Equation 2 by multiplying x by a power of 10 that moves the decimal point to the left of the repeating digits.
- Step D: Subtract Equation 2 from Equation 1. This cancels out the infinite decimal tail.
Let x = 0.6363…
Eq 1: Multiply by 100 (move dot past the first ’63’):
100x = 63.6363…
Eq 2: Multiply by 1 (dot is already before ’63’):
1x = 0.6363…
Subtract: (100x – 1x) = (63.63… – 0.63…)
99x = 63
3. Inch Fraction Rounding (For Makers & Builders)
In construction, exact decimals often don’t translate well to a tape measure. A standard decimal-to-fraction calculation might give you 191/217, which is mathematically correct but physically useless on a job site.
This tool includes a “Rounding Options” feature specifically for this purpose. It snaps the decimal to the nearest practical ruler mark (e.g., 1/16th or 1/32nd of an inch).
- 1/16: Standard precision for framing and general carpentry.
- 1/32 or 1/64: High precision for cabinetry, machining, and fine metalworking.
Common Decimal Conversions
| Decimal | Fraction | % Equivalent |
|---|---|---|
| 0.0625 | 1/16 | 6.25% |
| 0.125 | 1/8 | 12.5% |
| 0.166… | 1/6 | 16.6% |
| 0.25 | 1/4 | 25% |
| 0.333… | 1/3 | 33.3% |
| 0.375 | 3/8 | 37.5% |
| 0.5 | 1/2 | 50% |
| 0.625 | 5/8 | 62.5% |
| 0.75 | 3/4 | 75% |
| 0.875 | 7/8 | 87.5% |
Why use the Greatest Common Divisor (GCD)?
When you convert a decimal like 0.5, you initially get the fraction 5/10. While mathematically accurate, this is not the “standard” form. The standard form requires the fraction to be in its simplest terms.
To simplify, we find the GCD the largest number that divides evenly into both the numerator (top) and the denominator (bottom). For 5 and 10, the GCD is 5.
Sources: Calculator Soup, Calculator.net, RapidTables, Math Salamanders, Omni Calculator, AtoZ Math, Mouser Electronics, GraphCalc