Published 15 January 2026 · 6 min read
The Golden Rule
The precision of a converted value cannot exceed the precision of the input. If your input has two significant figures, your output should have at most two.
Example: A tape measure reads 1.5 meters. The mathematical conversion gives 4.921259842519685 feet. But writing the full value suggests your measurement was accurate to the nanometer — it wasn't. The honest answer is "about 4.9 feet".
Determine Input Precision
Ask yourself: how accurately was the input measured?
- 1.5 meters — two significant figures (uncertainty ±0.05 m).
- 1.50 meters — three significant figures (uncertainty ±0.005 m).
- 1.500 meters — four significant figures (uncertainty ±0.0005 m).
- 1.5 ± 0.1 meters — explicit uncertainty of ±0.1 m.
Typical precision of everyday measurements:
| Measurement | Typical precision | Significant figures |
|---|---|---|
| Distance by tape measure | ±1 mm to ±5 mm | 2–3 |
| Body weight by scale | ±0.1 kg | 3–4 |
| Temperature by thermometer | ±0.5 °C | 2–3 |
| GPS position | ±3 m | 4–5 |
| Speed limit sign | Exact by convention | N/A |
| Recipe ingredient | ±10% | 1–2 |
Match Output to Input
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 | 1–2 | 1–2 | "240 mL of milk" |
| Casual measurement | 2–3 | 2–3 | "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 |
Why This Matters
The most common mistake in conversion is over-precision. Displaying more digits than the input supports falsely suggests greater accuracy and can lead to incorrect decisions.
Example: Medical dosage
A patient weighs 70 kg (two significant figures). A drug dose is calculated at 15 mg/kg. The mathematically exact dose is 1,050 mg. But if the weight is only accurate to the nearest kilogram, the dose could reasonably range from 1,035 mg to 1,065 mg. Reporting "1,050 mg" without acknowledging the uncertainty misrepresents the precision.
Example: Construction
A room is measured as 12.5 ft × 15.5 ft. The area is 193.75 ft². Rounding to 194 ft² is appropriate — the input precision does not support four significant figures.
Example: Navigation
A GPS fix gives a position accurate to ±3 m. Reporting the position to six decimal places (which would be accurate to centimeters) misrepresents the actual precision.
Rounding Rules
The standard convention is "round half to even" (banker's rounding):
- If the digit after the last kept place is less than 5, round down.
- If the digit after is greater than 5, round up.
- If the digit after is exactly 5 (with nothing after it), round to the nearest even number.
So 2.5 rounds to 2, 3.5 rounds to 4, 4.5 rounds to 4, 5.5 rounds to 6. This avoids the upward bias of "round half up".
Significant Figures in Multiplication and Division
When multiplying or dividing, the result has the same number of significant figures as the input with the fewest significant figures. Since conversion is fundamentally multiplication or division by a factor, this rule applies directly.
- Input: 1.5 m (2 sig figs). Output: 4.9 ft (2 sig figs).
- Input: 12.30 m (4 sig figs). Output: 40.35 ft (4 sig figs).
Significant Figures in Addition and Subtraction
When adding or subtracting, the result is rounded to the same decimal place as the least precise input.
Example: 1.20 + 3.4 = 4.60, but since 3.4 has only one decimal place, the result is rounded to 4.6.
Scientific Notation for Extremes
For very large or very small values, scientific notation expresses both magnitude and precision clearly. For example:
- Avogadro's number: 6.022 × 10²³ per mole (4 significant figures).
- Elementary charge: 1.602 × 10⁻¹⁹ C (4 significant figures).
- Boltzmann constant: 1.381 × 10⁻²³ J/K (4 significant figures).
The number of digits in the coefficient directly states the precision.
How M-Convert Handles This
M-Convert displays results with an automatic significant-figure cap that scales with the input magnitude, typically showing about 10–12 significant figures. This provides enough digits for most users to round to their preferred precision without artificially truncating the result.
The full-precision internal calculation is never rounded mid-computation — rounding is applied only at display time. This gives users control over final precision while preserving the integrity of the calculation.
A Practical Checklist
Before reporting any converted value:
- What is the precision of the input?
- Does the output have more digits than the input supports?
- Is the context casual, technical, or scientific?
- Would extra digits mislead the reader?
- Is scientific notation appropriate?
Answering these questions ensures that converted values communicate appropriate precision, not artificial accuracy.