# Measurement and the Factor Label Method

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Measurement and the Factor Label Method
Chem 140

SI base units SI (Système Internationale d’Unites) adopted in 1960
Contains 7 base units: length: meter (m) mass: kilogram (kg) time: second (s) electrical current: ampere (A) temperature: kelvin (K) amount of substance: mole (mol) Luminous intensity: candela (Cd)

value (exp.) value tera- (T) 1012 1,000,000,000,000 giga- (G) 109 1,000,000,000 mega- (M) 106 1,000,000 kilo- (k) 103 1,000 deci- (d) 10-1 0.1 centi- (c) 10-2 0.01 milli- (m) 10-3 0.001 micro- (µ) 10-6 nano- (n) 10-9 pico- (p) 10-12

Derived units: speed 1 m s-1 1 meter… …in 1 second speed (velocity) 10
20 30 40 60 70 80 90 50 1 meter… …in 1 second 1 m s-1 speed (velocity)

Derived units: acceleration
speedometer m s-1 Start

Derived units: acceleration
1 meter per second per second 1 1 m s-2 speedometer m s-1 After 1 second

Acceleration – 6 m = s2 50 m/s… …to 20 m/s… …in 5 s change in speed
time = –30 m s 1 5 s acceleration = = – 6 m s2

Other derived units Force (newton, N): kg m s-2
Work, energy (joule, J): kg m2 s-2 Power (watt, W): kg m2 s-3 Pressure (pascal, Pa): kg m-1 s-2 Volume: m3 Density: kg m-3

Metric to English (Without Too Much Memorizing)
1 inch = 2.54 cm 1 gallon (US) = 231 in3 1 lb. = g °C = (°F – 32) x 5/9 °F = (°C x 9/5) + 32 You can figure out many other conversions from these basic (exact) ones

Factor-label method (on board)
Convert 65 mph to m s-1, using the information on the previous slide, and english-to-english conversions. A car gets 35 mpg fuel mileage. What’s this in km/L? cubic meters to cm3

Volume What is the volume of a cube 0.1 m (1 dm) on a side, in m3?
Also called a “liter” (L)

Volume What is the length of each side of a cube with a volume of 1 mL? 0.001 L = m3 = (0.01)3 m3 = 0.01 m (1 cm) on a side

1 m3 = 1 kL Length and Volume 1 Mg of water 1 cm3 1 kg of water = 1 mL
10 20 30 40 60 70 80 90 50 1 dm3 = 1 L 1 cm3 = 1 mL 1 kg of water 1 g of water 1 Mg of water

Volume and Mass Linear Cubic Liters Water 1 m 100 m 1 m3 100 m3 1 kL
1 Mg 1 dm 10-1 m 1 dm3 10-3 m3 1 L 100 L 1 kg 1 cm 10-2 m 1 cm3 10-6 m3 1 mL 10-3 L 1 g 1 mm 10-3 m 1 mm3 10-9 m3 1 µL 10-6 L 1 mg