What are significant figures anyway?
(According to Google search: What are significant figures)
Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
How do you know if a digit is a significant figure?
- It is a non-zero number. (e.g. 122 – 3 sf)
- It is a zero between non-zero numbers. (e.g. 102 – 3 sf)
- It is a final zero after a decimal point (e.g. 2.0 cm – 2 sf)
- In a number < 1, it is a zero after a non-zero number (e.g. 0.20 cm – 2 sf)
Not a significant figure:
- Leading zeros in a number < 1 (e.g. 0.002 cm – 1 sf)
- In a non-decimal number, final zeros may/may not be significant
e.g. 102000 cm – may be 3/4/5/6 sf depending on the original number it is derived from
102000.00 has 8 significant figures! (Refer to rule 3)
Exam format: How to use significant figures and decimal places in calculations?
The general rule is to round the answer to the least precise measurement used in
Addition/ Subtraction (+/-): Follow the term with the least number of decimal places
E.g. 3.55 cm + 0.1 cm = 3.7 cm NOT 3.65 cm
Multiplication/ Division (×/ ÷): Follow the term with the least number of significant figures
E.g. 4.0 m / 2 s = 2 m/s NOT 2.0 m/s
Ignore counting numbers:
e.g. 1000 cm / 24 –> The answer will be in 4 sf (following 1000 cm)
How to use significant figures in unit conversion?
Ensure that the converted figure has the same number of significant figures as the original figure.
e.g. 0.3 m = 30 cm (as 0.3 m only has 1 sf, the converted figure 30 cm only has 1 sf too)
0.30 m = 30 cm (since 0.30 m now has 2 sf, 30 cm has 2 sf as well)
Note: Assume that all digits are sf when the original figure has final zeros.
e.g. 50 mm = 0.050 m (2 sf)