BIZOMAT MAKEOS · Units
Decimal to Fraction
What is the nearest fraction to this decimal, and how far off is it?
Nearest fractional-inch size (to 1/8 … 1/128), the best fraction with a limited denominator (continued fractions) and the millimetre equivalent.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Decimal value | The decimal number, in inches for size work or a plain ratio. | |
| Fractional-inch resolution | choice | The smallest fraction step you can use, e.g. 1/64 for fractional drills. |
| Largest denominator for best fraction | Largest denominator allowed for the best-fraction approximation, e.g. the largest gear tooth count. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Decimal value
- What it is
- The decimal number to express as a fraction: a size in inches for drill, bar or tool selection, or a plain ratio.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.4375 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a size in millimetres, divide by 25.4 first to get inches.
What this means: Fractional-inch resolution
- What it is
- The finest fraction step you can actually use, for example the step between fractional drill or reamer sizes. The nearest fraction is rounded to this step.
- Units and format
- Choose one of 5 options from the list: 1/8; 1/16; 1/32; 1/64; 1/128.
- Example
- The form opens with “1/64” selected as a worked example. Choose the option that matches your case.
- Get it right
- A finer step gets closer to the value but may give a size you cannot buy.
What this means: Largest denominator for best fraction
- What it is
- The largest denominator allowed when the tool searches for the closest possible fraction, for example the largest gear tooth count available in a change-gear train.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 100000. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger limit allows a closer best fraction.
- Get it right
- Used only for the best-fraction result, not for the nearest fractional-inch size.
Method and formulas
- Nearest fraction = round(value × N) ÷ N, reduced to lowest terms.
- Best fraction: continued-fraction convergents and semiconvergents of the value, keeping the closest with denominator ≤ the limit.
- Millimetres = inches × 25.4.
- Example: 0.4375 is exactly 7/16 in (11.1125 mm).
Limitations
- Negative values are not accepted; convert the magnitude.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the nearest fractional drill or stock size
- Approximate a ratio with small whole numbers for change gears
- Convert inch decimals to millimetres
Who it is for
- Machinists
- Toolmakers
- Design engineers
What you get
- Nearest fraction at the chosen resolution and its error
- Best fraction with a limited denominator and its error
- Millimetre equivalent
Interpreting the result
- For ratios, check the error against the accuracy the job needs (e.g. thread pitch error over the thread length).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3, 11–13. Topic reference; no source tables or recommended settings are reproduced.
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