1.2.10Development of Practical Skills in Physics
Significant Figures
5 min read 5 parts Lesson 29 of 29 Unit quiz Virtual lab
Section 1 of 5Counting Significant Figures
Significant figures show how precisely a value is known, so they must be counted according to fixed rules.
Non-zero digits
- Every digit from 1 to 9 is significant, so 4.82 has three significant figures.
Zeros between digits
- A zero trapped between non-zero digits is significant, so 3007 has four significant figures.
Leading zeros
- Zeros at the start of a decimal only fix the position of the decimal point, so 0.0042 has two significant figures.
Trailing zeros
- Zeros after the decimal point at the end of a number are significant, so 2.50 has three significant figures.
Standard form
- Writing 4.50 × 10³ removes any doubt, because every digit in the coefficient is significant.
Section 2 of 5Rounding Correctly
1
Decide how many significant figures are needed, counting from the first non-zero digit on the left.
2
Look at the digit immediately after the last one you are keeping.
3
If that digit is 5 or more, round the last kept digit up; if it is 4 or less, leave it unchanged.
4
Keep the place value by adding zeros or using standard form, for example 15 840 to three figures is 1.58 × 10⁴.
5
Round only once, at the end of the calculation, and keep extra figures in intermediate steps to avoid rounding errors.
Section 3 of 5Significant Figures in Physics
Significant Figures in Physics
Calculations
- The answer should have no more significant figures than the least precise value used in the calculation.
Measurements
- The number of significant figures reflects the resolution of the instrument used to take the reading.
Consistency
- Readings of the same quantity, such as lengths from one ruler, should be given to the same number of decimal places.
Final answers
- Giving too many figures suggests a precision that the data do not have, while too few loses information.
| Value | Significant figures | Reason |
|---|---|---|
| 0.0560 | 3 | Leading zeros do not count, trailing zero does |
| 1002 | 4 | Zeros between digits count |
| 3.0 × 10⁸ | 2 | Both digits in the coefficient count |
Section 4 of 5Worked Example
Question
- A metal block has mass 24.3 g and volume 8.7 cm³.
- Calculate its density and give the answer to an appropriate number of significant figures.
- Use density = mass ÷ volume = 24.3 ÷ 8.7.
- The calculator gives 2.7931... g cm⁻³.
- The mass has three significant figures and the volume has two, so the answer can have only two.
Answer Density = 2.8 g cm⁻³ (2 significant figures).
Section 5 of 5Exam Checklist & Tips
1.2.10 – Key Points for the Exam
- Significant figure A digit in a number that carries meaning about its precision, counted from the first non-zero digit.
- Rounding Replacing a number with a simpler value with fewer figures, using the next digit to decide.
- Precision How closely repeated measurements agree, reflected by the number of significant figures.
- Standard form A number written as A × 10ⁿ with 1 ≤ A < 10.
- Resolution The smallest change in a quantity that an instrument can detect.
Common Mistakes
- Counting leading zeros in 0.0045 as significant figures.
- Rounding at every step of a calculation instead of only at the end.
- Giving a final answer with more significant figures than the data justify, just because the calculator shows them.
- Dropping a trailing zero such as writing 2.5 for 2.50 when the zero is part of the measurement.