To determine significant figures in a number, follow these basic rules:
- All nonzero digits are significant.
- Zeros between nonzero digits are significant.
- Leading zeros (zeros before the first nonzero digit) are not significant.
- Trailing zeros to the right of the decimal point are significant.
- Trailing zeros in a whole number with no decimal point are generally not significant unless specified by notation such as a decimal point or scientific notation.
For example:
- 123.45 has 5 significant figures (all digits are nonzero).
- 1002 has 4 significant figures (zeros are between nonzero digits).
- 0.00123 has 3 significant figures (leading zeros not significant).
- 12.300 has 5 significant figures (trailing zeros after decimal are significant).
- 1500 has 2 significant figures if no decimal point is shown (the trailing zeros are not significant).
When doing calculations:
- For addition/subtraction, the result is rounded to the smallest number of decimal places in the inputs.
- For multiplication/division, the result is rounded to the smallest number of significant figures in the inputs.
These rules help identify how many digits in a number are meaningful for precision in measurements or calculations.
