Significant Figures: Matter

What are Significant Figures? ● All those values in a measurement that are known with certainty and the first estimated or uncertain ● Proper measurements are made by reporting the measure one place beyond the graduations of the instruments

1. All non-zero numbers ARE significant 32.2 → 3 non-zero digits → 3 significant figures 45 → 2 non-zero digits → 2 significant figures 0.349 → 3 non-zero digits → 3 significant figures

2. Zeros between two non-zero digits ARE significant 2051 → 3 non-zero digits & 1 zero between 2 non-zero digits → 4 significant figures 10503 → 3 non-zero digits & 2 zero between 2 non-zero digits → 5 significant figures

3. Leading zeros are NOT significant Are only “place holders” → they are only there so that the actual numbers are in the right place value 0.54 → 2 non-zero digits & 1 initial zero holds ones place → 2 significant figures 0.0032 → 2 non-zero digits & 3 initial zeros holds ones, tenths, and hundredths place → still only 2 significant figures

4. Trailing zeros to the right of the decimal ARE significant They are NOT place holders, but an actual measured value of zero 92.00 → 2 non-zero digits and 2 trailing zeros → 4 significant digits 0.780 → 2 non-zero digits & 1 trailing zero → 3 significant figures

5. Trailing zeros in a whole number with a decimal shown ARE significant Decimal indicates the previous zero(s) are significant 540. → 2 non-zero digits, 1 trailing zero with decimal point → 3 significant figures 06700. → 2 non-zero digits, 2 trailing zeros with decimal point → 4 significant figures

6. Trailing zeros in a whole number with NO decimal shown ARE NOT significant No decimal indicates the trailing zero(s) are not significant 540 → 2 non-zero digits, 1 trailing zero with NO decimal point → 2 significant figures 06700 → 2 non-zero digits, 2 trailing zeros with NO decimal point → 2 significant figures

7. Exact numbers have an INFINITE number of significant figures This applies to numbers that are definitions 1 meter = 1.00 meters = 1.0000 meters = 1.0000000000000000000 meters, etc.

8. For a number in scientific notation: N x 10x, all digits comprising N ARE significant; "10" and "x" are NOT significant 5.02 x 104 → 2 non-zero digits, 1 middle zero → 3 significant figures