Measurements and solving problems

Standards of measurement

SI Units The 11th General Conference on Weights and Measures (1960) adopted the name Système International d'Unités (International System of Units, international abbreviation SI), for the recommended practical system of units of measurement. The 11th General Conference on Weights and Measures (1960) adopted the name Système International d'Unités (International System of Units, international abbreviation SI), for the recommended practical system of units of measurement.1960

Fundamental SI Units (p 32) Length – meter (m) Length – meter (m) Mass – kilogram (kg) Mass – kilogram (kg) Time – second (s) Time – second (s)

SI prefixes kilo (k) , 1000 kilo (k) , 1000 centi (c) , 1/100 centi (c) , 1/100 milli (m) , 1/1000 milli (m) , 1/1000 micro (  ) , 1/1,000,000 micro (  ) , 1/1,000,000 nano (n) , 1/1,000,000,000 nano (n) , 1/1,000,000,000 pico (p) , 1/1,000,000,000,000 pico (p) , 1/1,000,000,000,000

examples 1 millimeter (1 mm) = m 1 millimeter (1 mm) = m 1 nanoliter (1 nL) = 1 x L 1 nanoliter (1 nL) = 1 x L 1 kilometer (1 km) = 1000 m 1 kilometer (1 km) = 1000 m

English - Metric conversions 1 inch = 2.54 cm 1 inch = 2.54 cm 1 mile = 1.61 km 1 mile = 1.61 km 1 pound = 0.45 kg 1 pound = 0.45 kg 1 quart = 0.95 L 1 quart = 0.95 L

Factor Label method 250 mL = ? L 1000 mL = 1 L 250 mL x 250 mL x 1L 1000 mL = 1000 mL = 250 mL x 1L 1000 mL = 0.25 L 1000 mL = 0.25 L

2.1 m = ? cm 1 m = 100 cm 2.1 m x 2.1 m x 100 cm 1 m = 1 m = 2.1 m x 100 cm 1 m = 210 cm 1 m = 210 cm

Derived SI Units Volume – liter (L) Volume – liter (L) Density (mass per unit volume) Density (mass per unit volume) –g/ cm 3 –Density = mass/ volume – d = m/v

Density = 10.0 g/ cm 3 Density = 10.0 g/ cm 3 Volume = 2.0 cm 3 Volume = 2.0 cm 3 Mass = ? Mass = ? d = m/v m = d x v = (10.0 g/ cm 3 ) (2.0 cm 3 ) = 20. g

Measurement of volume by water displacement Eureka ('Eureka!', or 'Heureka'; Greek ηὕρηκα (later εὕρηκα); is a famous exclamation attributed to Archimedes. He reportedly uttered the word when he suddenly understood that the volume of an irregular object could be calculated by finding the volume of water displaced when the object was submerged in water, subsequently leaping out of his bathtub and running through the streets of Syracuse naked. Archimedesvolume SyracuseArchimedesvolume Syracuse

temperature Avg. KE of particles in a sample of matter Avg. KE of particles in a sample of matter

heat Sum total of KE of particles in a sample of matter Sum total of KE of particles in a sample of matter

Temperature scales Celsius ( o C) Celsius ( o C) Kelvin (K) Kelvin (K) T(K)= t( o C) +273 T(K)= t( o C) +273

Units of heat Joule (J) Joule (J) Calorie (cal) Calorie (cal) 1 cal = J 1 cal = J E value of food reported in kcal (called calories) E value of food reported in kcal (called calories)

accuracy Closeness of measurement to accepted value Closeness of measurement to accepted value

precision Agreement of values Agreement of values

Accuracy and precision Accuracy and precision

% error Value accepted - Value experimental Value accepted - Value experimental __________________________ x 100% __________________________ x 100% Value accepted Value accepted

Significant figures

Measurement of all digits known with certainty + one uncertain final digit Measurement of all digits known with certainty + one uncertain final digit

How many sig figs? (3) (5) (1) (2) (6)

Sig figs: addition and subtraction Round off so that final digit is in the same place as leftmost uncertain digit Round off so that final digit is in the same place as leftmost uncertain digit ________

Sig figs: multiplying and dividing Round off to the # of digits in the number w/ fewest sig figs Round off to the # of digits in the number w/ fewest sig figs x2.0 x2.0_____

Exact conversion factors DO NOT limit # of digits Exact conversion factors DO NOT limit # of digits

Scientific notation pp –789, x x 10 5 – x x 10 -4

Direct proportion (relationship)

Inverse proportion (relationship)