Measurements and solving problems Standards of measurement

Measurements and Measurements and solving problemssolving problems

Standards of measurementStandards of measurement

SI UnitsSI Units

• The 11th General Conference on The 11th General Conference on Weights and Measures (Weights and Measures (19601960) ) adopted the name adopted the name Système Système International d'UnitésInternational d'Unités (International (International System of Units, international System of Units, international abbreviation SI), for the abbreviation SI), for the recommended practical system of recommended practical system of units of measurement. units of measurement.

Fundamental SI Units (p 32)Fundamental SI Units (p 32)

• Length – meter (m)Length – meter (m)

• Mass – kilogram (kg)Mass – kilogram (kg)

• Time – second (s)Time – second (s)

SI prefixesSI prefixes

• kilo (k) - 10kilo (k) - 1033, 1000, 1000

• centi (c) - 10centi (c) - 10-2-2, 1/100, 1/100

• milli (m) - 10milli (m) - 10-3-3, 1/1000, 1/1000

• micro (micro () - 10) - 10-6-6, 1/1,000,000, 1/1,000,000

• nano (n) - 10nano (n) - 10-9-9, 1/1,000,000,000, 1/1,000,000,000

• pico (p) - 10pico (p) - 10-12-12, , 1/1,000,000,000,0001/1,000,000,000,000

examplesexamples

• 1 millimeter (1 mm) = 0.001 m1 millimeter (1 mm) = 0.001 m

• 1 nanoliter (1 nL) = 1 x 101 nanoliter (1 nL) = 1 x 10-9-9 L L

• 1 kilometer (1 km) = 1000 m1 kilometer (1 km) = 1000 m

English - Metric English - Metric conversionsconversions

• 1 inch = 2.54 cm1 inch = 2.54 cm

• 1 mile = 1.61 km1 mile = 1.61 km

• 1 pound = 0.45 kg1 pound = 0.45 kg

• 1 quart = 0.95 L1 quart = 0.95 L

Factor Label methodFactor Label method

250 mL = ? L250 mL = ? L1000 mL = 1 L1000 mL = 1 L250 mL x 250 mL x 250 mL x 1L 250 mL x 1L 1000 mL =1000 mL =250 mL x 1L 250 mL x 1L 1000 mL 1000 mL = 0.25 L= 0.25 L

2.1 m = ? cm2.1 m = ? cm

1 m = 100 cm1 m = 100 cm

2.1 m x 2.1 m x

2.1 m x 100 cm2.1 m x 100 cm

1 m =1 m =

2.1 m x 100 cm2.1 m x 100 cm

1 m = 1 m = 210 cm210 cm

Derived SI UnitsDerived SI Units

• Volume – liter (L)Volume – liter (L)

• Density (mass per unit volume)Density (mass per unit volume)– g/ cmg/ cm33

– Density = mass/ volumeDensity = mass/ volume– d = m/vd = m/v

• Density = 10.0 g/ cmDensity = 10.0 g/ cm33

• Volume = 2.0 cmVolume = 2.0 cm33

• Mass = ?Mass = ?

d = m/vd = m/v

m = d x vm = d x v

= (10.0 g/ cm= (10.0 g/ cm33) (2.0 cm) (2.0 cm33))

= = 20. g20. g

Measurement of volume Measurement of volume by water displacementby water displacement

EurekaEureka ('Eureka!', or 'Heureka'; Greek ('Eureka!', or 'Heureka'; Greek ηὕρηκα (later εὕρηκα); is a famous ηὕρηκα (later εὕρηκα); is a famous

exclamation attributed to exclamation attributed to ArchimedesArchimedes. . He reportedly uttered the word when he He reportedly uttered the word when he suddenly understood that the suddenly understood that the volumevolume of of an irregular object could be calculated an irregular object could be calculated

by finding the by finding the volumevolume of water of water displaced when the object was displaced when the object was

submerged in water, subsequently submerged in water, subsequently leaping out of his bathtub and running leaping out of his bathtub and running through the streets of through the streets of SyracuseSyracuse naked. naked.

temperaturetemperature

• Avg. KE of particles Avg. KE of particles in a sample of in a sample of mattermatter

heatheat

• Sum total of KE of Sum total of KE of particles in a particles in a sample of mattersample of matter

Temperature scalesTemperature scales

• Celsius (Celsius (ooC)C)

• Kelvin (K)Kelvin (K)

• T(K)= t(T(K)= t(ooC) +C) +273273

Units of heatUnits of heat

• Joule (J)Joule (J)

• Calorie (cal)Calorie (cal)

• 1 cal = 4.184 J1 cal = 4.184 J

• E value of food E value of food reported in kcal reported in kcal (called calories)(called calories)

accuracyaccuracy

• Closeness of Closeness of measurement to measurement to accepted valueaccepted value

precisionprecision

• Agreement of Agreement of valuesvalues

• Accuracy and Accuracy and precisionprecision

% error% error

• Value Value accepted accepted - - ValueValue experimental experimental

__________________________ __________________________ x 100%x 100%

ValueValue accepted accepted

Significant figuresSignificant figures

Significant figuresSignificant figures

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

How many sig figs?How many sig figs?

• 33.433.4

(3)(3)• 1004.11004.1

(5)(5)• 90000009000000

(1)(1)• 0.00000720.0000072

(2)(2)• 82.600082.6000

(6)(6)

Sig figs: addition and Sig figs: addition and subtractionsubtraction

• Round off so that final digit is in the Round off so that final digit is in the same place as leftmost uncertain same place as leftmost uncertain digitdigit 410.14410.1433 3322+________+________ 444422.143.143

442442

Sig figs: multiplying and Sig figs: multiplying and dividingdividing• Round off to the # of digits in the Round off to the # of digits in the

number w/ fewest sig figsnumber w/ fewest sig figs 14.0014.00

xx2.02.0

__________

28.0028.00

2828

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

Scientific notation pp 52-53Scientific notation pp 52-53

– 789,000.0789,000.0

7.890000 x 107.890000 x 1055

– 0.0007430.000743

7.43 x 107.43 x 10-4-4

Direct proportion Direct proportion (relationship)(relationship)

Inverse proportion Inverse proportion (relationship)(relationship)