Significant Measurements -significant figures are a way to report scientific values -significant figures are useful for expressing certainty ie. A length of 6.36 cm – last digit “6” is a guess or estimate Rules for Significant Figures -zeroes appearing between nonzero digits are significant ex. 40.7 L = 3 sig figs 87.009 km = 5 sig figs
Significant Measurements -zeroes appearing in front of non zero digits are not significant ex. 0.095897 m = 5 sig figs 0.0009 kg = 1 sig fig -zeroes at the end of a number and to the right of the decimal are significant ex. 85.00 = 4 sig figs 9.000000000 = 10 sig figs -zeroes at the end of a number, but BEFORE/LEFT OF the decimal may or may not be significant. It depends if you SEE the decimal. ex. 2000 m = 1 sig fig 2000. m = 4 sig figs
Significant Measurements Adding or Subracting Significant Figures -When adding or subtracting, the answer must have the same number of digits to the right of the decimal point as the measurement with the fewest digits to the right of the decimal point. ex. 25.1 g + 2.03 g + 0.015 g = 27.145 w/ significant figures = 27.1 Multiplying or Dividing Significant Figures -When multiplying or dividing, the answer should have no more significant figures than the measurement with the fewest number of significant figures ex. 3.05 g ÷ 8.472 mL = 0.360009443 g/mL w/ significant figures = 0.360 g/mL
Significant Measurements Scientific Notation -scientific notation can be used to shorten very large or very small numbers -scientific notation can be used in conjunction with significant figures -many scientific notations use two or three significant figures ex. 3,957,309,204 becomes 3.96 × 109 0.00000000007483 becomes 7.48 × 10-11 -the exponent by the “10” is determined by how many decimal places must be moved
Significant Figures Practice Write down the numbers and how many significant figures each one has as well as what kind of quantity is being measured (ie. mass, pressure, length, temperature, volume, etc): 1. 28.6 g 2. 3440. L 3. 910°C 4. 0.04604 atm 5. 0.006700 kg