To find the number of significant figures in a number, follow these rules:
- All nonzero digits are significant. For example, 123 has 3 significant figures.
- Zeros between nonzero digits are significant. For example, 1002 has 4 significant figures.
- Leading zeros (zeros before the first nonzero digit) are not significant. For example, 0.0045 has 2 significant figures.
- Trailing zeros are significant only if the number contains a decimal point. For example, 45.00 has 4 significant figures, but 4500 (without a decimal) has only 2 significant figures.
- If a number has a decimal point, all zeros after the last nonzero digit are significant. For example, 0.0700 has 3 significant figures
Steps to determine significant figures:
- Identify the first nonzero digit; this marks the start of significant figures.
- Count all digits from this first nonzero digit to the end, including zeros that meet the rules above.
- Use scientific notation if needed to clarify which zeros are significant.
Example:
- 0.00520 has 3 significant figures (5, 2, and the trailing zero because of the decimal point).
- 3500 has 2 significant figures if no decimal point is shown.
When performing calculations, the number of significant figures in the result depends on the operation:
- For addition/subtraction, round the result to the least number of decimal places in the inputs.
- For multiplication/division, round the result to the least number of significant figures in the inputs
This method ensures that the precision of the measurement is accurately reflected in the number of significant figures reported
