The Core Principle
Precision cannot be created by arithmetic. If you measure a table as "1.5 meters" (two significant figures), converting it to feet gives you a value you know only to two significant figures — about 4.9 feet. Writing "4.921259842519685" pretends you know the value to the nanometer, which you don't.
The rule: the precision of a converted value cannot exceed the precision of the input.
Determining Input Precision
Ask yourself: how accurately was the input measured or specified?
- 1.5 meters — two significant figures (uncertainty of ±0.05 m).
- 1.50 meters — three significant figures (uncertainty of ±0.005 m).
- 1.500 meters — four significant figures (uncertainty of ±0.0005 m).
- 1.5 m ± 0.1 — explicit uncertainty of ±0.1 m.
In everyday measurement (tape measure, kitchen scale, weather station), typical precision is:
- Length by tape measure: 2–3 significant figures.
- Mass by kitchen scale: 3–4 significant figures.
- Temperature: 2–3 significant figures.
- Speed by GPS: 3–4 significant figures.
Scientific instruments can measure to much higher precision, but that precision is documented with the measurement.
Choosing Output Precision
Once input precision is known, output precision follows:
| Context | Input sig figs | Output sig figs | Example |
|---|---|---|---|
| Rough estimate | 1 | 1–2 | "About 5 miles" |
| Everyday (cooking, travel) | 2 | 2 | "4.9 feet" |
| Casual measurement | 3 | 3 | "4.92 feet" |
| Consumer product specs | 3 | 3–4 | "4.921 feet" |
| Scientific measurement | 4+ | same as input | "4.9213 feet" |
| Engineering calculation | documented | match input uncertainty | Per spec |
Displayed vs Meaningful Digits
M-Convert displays results with an automatic significant-figure cap that scales with the input magnitude. This is a compromise: it shows enough precision for most users without pretending to a level of accuracy that does not exist.
Examples:
- Input 1.5 (2 sig figs) → output might show 4.9213 (5 sig figs). The extra digits are useful for the user who wants to round to a preferred precision.
- Input 1.523 (4 sig figs) → output shows 4.9967 (5 sig figs). The input's 4 sig figs are preserved in the output.
You, the user, choose the final displayed precision by rounding. M-Convert provides extra digits so you can round cleanly.
Practical Rules by Context
Everyday life
- Distance for driving: 1–2 decimal places on miles or kilometers.
- Weight for cooking: 0 decimal places on grams, 1 on ounces.
- Temperature for weather: 0 decimal places (°C or °F).
- Room dimensions: 1–2 decimal places on meters or feet.
- Shopping measurements: 0 decimal places on centimeters or inches.
Technical work
- Engineering drawings: specified to 2–3 decimal places (usually mm or thousandths of an inch).
- Laboratory measurements: match the instrument's documented precision.
- Scientific publications: follow the journal's conventions, typically 3–5 sig figs.
- Pharmaceutical dosing: usually specified explicitly to avoid rounding errors.
Financial and legal
- Currency: 2 decimal places (or the currency's smallest unit).
- Land area: 2–4 decimal places on acres or hectares.
- Freight weights: 0–2 decimal places on kg or lb.
Worked Examples
Example 1: Body weight conversion
A scale reads 70.2 kg. Convert to pounds.
- Exact conversion: 70.2 × 2.2046226218487757 = 154.76450885398408 lb.
- Appropriate output: 154.8 lb (one decimal place matches the 3-significant-figure input precision).
- Inappropriate: 154.76450885398408 lb — the input does not support this many digits.
Example 2: Engineering dimension
A CAD drawing specifies 45.72 mm. Convert to inches.
- Exact: 45.72 ÷ 25.4 = 1.8 in exactly.
- Appropriate output: 1.800 in (matching the 4-significant-figure input).
- If the drawing specifies "45.7 mm" (3 sig figs), output is 1.80 in.
Example 3: Speed limit
A speed limit sign in the EU says "100" (km/h). Convert to mph.
- Exact: 100 × 0.621371192237334 = 62.1371192237334 mph.
- Appropriate output: 62 mph (the input is exact by convention, but the convention itself only commits to a specific road speed, not a precise measurement).
Example 4: Scientific measurement
A spectroscopy measurement gives a wavelength of 656.28 nm (5 sig figs). Convert to Å (1 Å = 0.1 nm).
- Exact: 656.28 ÷ 0.1 = 6,562.8 Å.
- Appropriate output: 6,562.8 Å (5 sig figs preserved).
When to Round
Round at the end of the calculation, not at every step. Intermediate rounding accumulates error. M-Convert keeps full precision internally and rounds only for display.
The standard rounding rule is "round half to even" (banker's rounding), which avoids the upward bias of "round half up".
See the Significant Figures and Rounding guide for details.
How M-Convert Handles This
- Full-precision internal computation. The engine computes using IEEE 754 double-precision floats (about 15–16 significant digits).
- Automatic significant-figure cap. The displayed value is limited to a significant-figure count that scales with magnitude, typically 10–12 significant figures, ensuring clean rounding for the user.
- Scientific notation for extremes. Very large or small results are displayed in scientific notation to make the scale clear.
- No silent rounding. The engine does not round results before display; the user decides the final precision.
Summary
- Match output precision to input precision.
- Round only at the end, not during intermediate steps.
- Use 2–3 significant figures for everyday purposes, 4+ for technical work.
- Be honest about uncertainty: it is better to report "about 4.9" than "4.9212598425".
- Use M-Convert's full-precision results and round them yourself to the precision you need.