22 Rules for Counting Significant Figures Significant & Non-significant zerosLeading zeros, precede non-zero digits = nonsignificantExample: = 2 s.f. - zeros are non-significantCaptive zeros (between nonzero digits) = significantExample: (4 s.f. - all numbers are significant)Trailing zeros (right end of number)Significant if bar is placed over zero or over zero to rightExample: 200 (only #2 is significant = 1 s.f.)2Ō0 (2 s.f. - 2 & Ō both significant)20Ō (3 s.f. - 2 and both zeros are significant)Following decimal to right of nonzero digit = significant5.00 = 3 s.f.
23 Rules for counting significant figures (continued) All nonzero integers are significantExample: 1457 has 4 s.f.Exact numbers have unlimited number of s.f.Determined by counting8 apples, 21 studentsNot obtained from measuring devicesFrom definitions1 inch is exactly 2.54 cmWill not limit numbers in calculationsUse same rules for scientific notation (10x not s.f.)
24 To give answer with correct number of significant figures – round off Look at number to right of last s.f.If number is <5 round downIf number is ≥5 round upDo not round off until end of calculations
25 Rules for s.f. in calculations Multiplication & DivisionAnswer should have same number of s.f. as measurement with smallest number of s.f.Example: 4.56 x 1.4 = → 6.4(3 s.f.) (2 s.f.)* (2 s.f.)*Addition & SubtractionLimited by smallest number of decimal placesExample: (2 decimal places)(1 decimal place)*(3 decimal places)→ (1 decimal place)*
28 Converting between Kelvin & Celsius To convert from Kelvin to Celsius:T°C = TK – 273Liquid Nitrogen boils at 77K, what is this in Celsius?T°C = 77 – 273 = -196 °CTo convert from Celsius to Kelvin:TK = T°CThe bp of water on top of Mt. Everest is 70 °C. Convert to K.TK = = 343 K
32 Density: amount of matter in a given volume of substance Density = mass / volumeDetermine mass using a balanceDetermine volume by calculations, graduated cylinder, or water displacementUnits are in g/cm3, g/mL, kg/L, lb/gal