Significant Figures:
Significant figures (digits) are used when you are working with data that has been measured. It is important to examine them when you are doing calculations using numbers obtained from a measurement. Knowing about sig figs allows you to ROUND your answer correctly.
Five Rules for determining the number of Significant Figures in a Measurement:
1) All nonzero integers are significant.
Ex: 456 cm 456 cm has 3 sig figs
2) All zeros to the left of the first nonzero digit are not significant since they are used to locate the decimal point.
Ex: 0.00567 kg 0.00567 kg has 3 sig figs
3) All zeros between nonzero digits are significant.
Ex: 207.08 cm 207.08 cm has 5 sig figs
Ex: 0.0401 L 0.0401 L has 3 sig figs
4) All zeros at the end of a number that has a decimal point are significant.
Ex: 34.070 mg 34.070 mg has 5 sig figs
Ex: 0.0670 g 0.0670 g has 3 sig figs
Ex: 400. mm 400. mm has 3 sig figs
5) Numbers that are not measurements have an infinite number of sig figs.
Ignore them when your trying to decide how many significant figures you need to round.
Adding/Subtracting with Significant Figures:
When adding or subtracting, round your answer to the least number of decimal places.
Ex: 32.3 + 51 = 83.2 --> 83
Ex: 452.99 + 1.120005 = 453.110005 --> 453.11
Multiplication/Division with Significant Figures:
When multiplying or dividing, round your answer to the least number of sig figs.
Ex: 0.0025 × 3568 = 8.92 --> 8.9
Ex: 6.35 × 3098 × 25 = 491807.5 --> 4.9×10⁵
Ex: 4525 ÷ 320 = 14.140625 --> 14
Ex: (1.234×10⁴) × (83.4×10⁻²) = 3430.52 --> 3.4×10³
3.0
Five Rules for determining the number of Significant Figures in a Measurement:
1) All nonzero integers are significant.
Ex: 456 cm 456 cm has 3 sig figs
2) All zeros to the left of the first nonzero digit are not significant since they are used to locate the decimal point.
Ex: 0.00567 kg 0.00567 kg has 3 sig figs
3) All zeros between nonzero digits are significant.
Ex: 207.08 cm 207.08 cm has 5 sig figs
Ex: 0.0401 L 0.0401 L has 3 sig figs
4) All zeros at the end of a number that has a decimal point are significant.
Ex: 34.070 mg 34.070 mg has 5 sig figs
Ex: 0.0670 g 0.0670 g has 3 sig figs
Ex: 400. mm 400. mm has 3 sig figs
5) Numbers that are not measurements have an infinite number of sig figs.
Ignore them when your trying to decide how many significant figures you need to round.
Adding/Subtracting with Significant Figures:
When adding or subtracting, round your answer to the least number of decimal places.
Ex: 32.3 + 51 = 83.2 --> 83
Ex: 452.99 + 1.120005 = 453.110005 --> 453.11
Multiplication/Division with Significant Figures:
When multiplying or dividing, round your answer to the least number of sig figs.
Ex: 0.0025 × 3568 = 8.92 --> 8.9
Ex: 6.35 × 3098 × 25 = 491807.5 --> 4.9×10⁵
Ex: 4525 ÷ 320 = 14.140625 --> 14
Ex: (1.234×10⁴) × (83.4×10⁻²) = 3430.52 --> 3.4×10³
3.0
Uncertainty:
Uncertainty is when a quantity has been measured with an instrument. Its measurement is a result of the instrument used or of the skill of the person taking the measurement.
There are 2 ways of expressing uncertainty:
1) Absolute uncertainty: which is expressed in the same units as the measurement.
Ex: 3.4cm ± 0.5cm
2) Relative uncertainty: which is expressed as a percentage of the measurement.
Ex: 3.4cm ± 5%
Relative uncertainty = Absolute uncertainty x 100
Value of measurement
*Be sure to remember that the uncertainty should have the same number of decimals as the measurement*
There are 2 ways of finding the uncertainty:
1) It could be written on the instrument itself.
2) If not, the uncertainty is equal to one half of the smallest measurement provided by the instrument.
There are 2 ways of expressing uncertainty:
1) Absolute uncertainty: which is expressed in the same units as the measurement.
Ex: 3.4cm ± 0.5cm
2) Relative uncertainty: which is expressed as a percentage of the measurement.
Ex: 3.4cm ± 5%
Relative uncertainty = Absolute uncertainty x 100
Value of measurement
*Be sure to remember that the uncertainty should have the same number of decimals as the measurement*
There are 2 ways of finding the uncertainty:
1) It could be written on the instrument itself.
2) If not, the uncertainty is equal to one half of the smallest measurement provided by the instrument.
Ex:
73.00mL ± 0.05mL
73.00 mL ± 0.1%
73.00 mL ± 0.1%