Significant figures
Every measurement has limited precision. Significant figures are the digits that are actually known, plus one estimated digit.
Rules for counting them:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant: 1002 has 4.
- Leading zeros are never significant: 0.0052 has 2.
- Trailing zeros are significant only if the number has a decimal point: 2.50 has 3, but 2500 has 2.
Calculating with significant figures
- Multiplying or dividing: the answer gets as many significant figures as the measurement with the fewest.
- Adding or subtracting: the answer gets as many decimal places as the measurement with the fewest.
Worked example: 4.56 × 1.4
The calculator shows 6.384. The factors have 3 and 2 significant figures, so the answer gets 2.
6.4
Common mistake
Counting leading zeros. In 0.0052 the zeros only locate the decimal point. Written in scientific notation, 5.2 × 10−3, they disappear, which shows they were never significant.