Significant Figures
Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. They are used in science and engineering to communicate how accurately a value has been measured.
Rules for Counting Significant Figures
| Rule | Example | Sig Figs |
|---|---|---|
| All non-zero digits are significant | 4,782 | 4 |
| Zeros between non-zero digits are significant | 5,008 | 4 |
| Trailing zeros after a decimal point are significant | 3.500 | 4 |
| Leading zeros (before the first non-zero digit) are NOT significant | 0.0042 | 2 |
| Trailing zeros in a whole number (ambiguous without decimal point) | 3,600 (ambiguous) | 2, 3 or 4 |
Rounding to Significant Figures
- Count from the first non-zero digit to the required number of sig figs.
- Look at the next digit: if 5–9, round up; if 0–4, round down.
- Replace all subsequent digits with zeros (whole numbers) or drop them (decimals).
Worked Examples
| Number | Round to | Result |
|---|---|---|
| 73,462 | 3 sig figs | 73,500 |
| 0.004826 | 2 sig figs | 0.0048 |
| 9.9975 | 4 sig figs | 10.00 |
| 150,800 | 3 sig figs | 151,000 |
Why Significant Figures Matter
Suppose you measure a room as 5 m wide and a tile as 0.3 m. Dividing: 5 ÷ 0.3 = 16.666... – but your measurement was only accurate to 1 sig fig, so the answer should be stated as 17, not 16.666.
Significant figures ensure that a calculated answer does not claim more accuracy than the original measurements justify.
- Non-zero digits are always significant.
- Zeros between non-zeros are always significant.
- Leading zeros are never significant.
- Trailing zeros after the decimal point are significant.
- When rounding, do not claim more sig figs than your least precise measurement.
Quick Practice
- How many significant figures does 0.00503 have?
- Round 86,350 to 2 significant figures.
- How many sig figs in 4.700?
- Round 0.09846 to 3 significant figures.
- A scientist records 1.20 kg. How many significant figures is this?
Summary
Significant figures express the precision of a measurement. By carefully counting and rounding to the correct number of sig figs, scientists and engineers avoid overstating the accuracy of their results. Mastering sig figs is essential for chemistry, physics, engineering, and any data-driven field.