Convert millimeters to decimal inches, round to a chosen ruler subdivision, and measure the rounding error. Animated subdivisions show why precision changes the answer.
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The calculation
Inches = mm ÷ 25.4; numerator = round(inches × denominator)
Worked example
10 mm ÷ 25.4 = about 0.393701 in. At sixteenths, round 0.393701 × 16 to 6, giving 6/16 = 3/8 in. That represents 9.525 mm, 0.475 mm below the original. At sixty-fourths, 25/64 in represents 9.921875 mm, about 0.078 mm below 10 mm.
Choose the denominator from the required tolerance. The inch-to-millimeter conversion is exact; selecting a fraction usually introduces rounding.
Video chapters
- 0:00 — 10 mm is about which inch fraction?
- 0:12 — Divide by 25.4 first
- 0:27 — Count sixteenth-inch steps
- 0:43 — Round 6.30 to 6; simplify 6/16
- 0:56 — Check the size of the rounding error
- 1:12 — A finer denominator can change the answer
- 1:26 — Separate whole inches for longer lengths
- 1:42 — Convert, choose precision, round, simplify
Read the full transcript
You have a ten-millimeter measurement, but your ruler is marked in fractions of an inch. Which mark is closest? There are two steps: convert to decimal inches, then choose how fine a fraction you want. That second choice changes the rounding.
One inch is exactly twenty-five point four millimeters. Divide ten by twenty-five point four. The result is approximately zero point three nine three seven inches. Keep extra decimal places for the next operation instead of rounding the intermediate result too early.
Suppose the ruler uses sixteenths. Each inch is divided into sixteen equal intervals. Multiply the decimal-inch value by sixteen to find how many intervals the measurement spans. Ten millimeters corresponds to approximately six point three of those sixteenth-inch steps.
Round that interval count to the nearest whole number: six. The fraction is six sixteenths of an inch. Divide numerator and denominator by two to simplify it to three eighths. The measurement has not changed; the selected ruler mark is an approximation.
Convert three eighths of an inch back to millimeters. Zero point three seven five times twenty-five point four equals nine point five two five millimeters. That is zero point four seven five millimeters below ten. Whether that difference is acceptable depends on the job's tolerance.
Try sixty-fourths instead. Multiply the unrounded inch value by sixty-four, giving about twenty-five point two. Round to twenty-five sixty-fourths. Converted back, that is about nine point nine two two millimeters, much closer to ten in this example.
For a longer measurement, separate whole inches after rounding the total interval count. A count of twenty-two sixteenths is one whole inch plus six sixteenths, or one and three eighths inches. Simplifying a fraction preserves its value; rounding is the step that introduces error.
The method is: divide millimeters by twenty-five point four, multiply by the chosen denominator, round the interval count, and simplify. Then check the error in the original units. Ten millimeters is about three eighths to the nearest sixteenth, or twenty-five sixty-fourths with a finer ruler.