Rules for Counting Significant Figures Significant & Non-significant zeros Leading zeros, precede non-zero digits = nonsignificant Example: = 2 s.f. - zeros are non-significant Captive zeros (between nonzero digits) = significant Example: (4 s.f. - all numbers are significant) Trailing zeros (right end of number) Significant if bar is placed over zero or over zero to right Example: 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 = significant 5.00 = 3 s.f.
Rules for counting significant figures (continued) All nonzero integers are significant Example: 1457 has 4 s.f. Exact numbers have unlimited number of s.f. Determined by counting 8 apples, 21 students Not obtained from measuring devices From definitions 1 inch is exactly 2.54 cm Will not limit numbers in calculations Use same rules for scientific notation (10 x not s.f.)
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 down If number is ≥5 round up Do not round off until end of calculations
Rules for s.f. in calculations Multiplication & Division Answer 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 & Subtraction Limited by smallest number of decimal places Example: (2 decimal places) 18.0 (1 decimal place)* (3 decimal places) → 31.1 (1 decimal place)*
Converting between Kelvin & Celsius To convert from Kelvin to Celsius: T °C = T K – 273 Liquid Nitrogen boils at 77K, what is this in Celsius? T °C = 77 – 273 = -196 °C To convert from Celsius to Kelvin: T K = T °C The bp of water on top of Mt. Everest is 70 °C. Convert to K. T K = = 343 K
Density: amount of matter in a given volume of substance Density = mass / volume Determine mass using a balance Determine volume by calculations, graduated cylinder, or water displacement Units are in g/cm 3, g/mL, kg/L, lb/gal