The Metric The Metric SystemSystem

UNITS OF UNITS OF MEASUREMENTMEASUREMENT

Use Use SI unitsSI units — based on the metric — based on the metric systemsystem

Length Length

MassMass

VolumeVolume

TimeTime

TemperatureTemperature

meter, mmeter, m

kilogram, kgkilogram, kg

seconds, sseconds, s

Celsius degrees, ˚CCelsius degrees, ˚Ckelvins, Kkelvins, K

liter, Lliter, L

Mass vs. WeightMass vs. WeightMass: Amount

of matter (grams, measured with a BALANCE)

Weight: Force exerted by the mass, only present with gravity

Can you hear Can you hear me now?me now?

Uncertainty in MeasurementUncertainty in Measurement

2 Reasons: ◦instruments aren’t flawless ◦measuring involves estimation (last digit)

Reliability of measurements can be checked 2 ways:◦Precision: same result obtained over and over

again◦Accuracy: how close the obtained value is to

the accepted value

Metric PrefixesMetric Prefixes

EqualitiesEqualities

State the same measurement in two State the same measurement in two different unitsdifferent units

lengthlength

10.0 in.10.0 in.

25.4 cm25.4 cm

DENSITYDENSITY

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

Mercury

13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33

Aluminum

2.7 g/cm2.7 g/cm33

Platinum

Solving CalculationsSolving Calculations

StrategyStrategy1. Get dimensions in common units.1. Get dimensions in common units.

2.2. Calculate volume in cubic Calculate volume in cubic centimeters.centimeters.

3. Calculate the density.3. Calculate the density.

ProblemProblem A piece of copper has a A piece of copper has a mass of 57.54 g. It is 9.36 cm long, mass of 57.54 g. It is 9.36 cm long, 7.23 cm wide, and 0.95 mm thick. 7.23 cm wide, and 0.95 mm thick. Calculate density (g/cmCalculate density (g/cm33).).

Density mass (g)volume (cm3)

Density mass (g)volume (cm3)

Volume DisplacementVolume Displacement

A solid displaces a matching volume of A solid displaces a matching volume of water when the solid is placed in water.water when the solid is placed in water.

33 mL33 mL25 mL 25 mL

Temperature ScalesTemperature ScalesFahrenheitFahrenheitCelsiusCelsiusKelvinKelvin

Anders Celsius1701-1744

Lord Kelvin(William Thomson)1824-1907

Temperature ScalesTemperature Scales

Notice that 1 kelvin = 1 degree Celsius1 kelvin = 1 degree Celsius

Boiling point Boiling point of waterof water

Freezing point Freezing point of waterof water

CelsiusCelsius

100 ˚C100 ˚C

0 ˚C0 ˚C

100˚C100˚C

KelvinKelvin

373 K373 K

273 K273 K

100 K100 K

FahrenheitFahrenheit

32 ˚F32 ˚F

212 ˚F212 ˚F

180˚F180˚F

Calculations Using Calculations Using TemperatureTemperature

Generally require temp’s in Generally require temp’s in kelvinskelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

Generally require temp’s in Generally require temp’s in kelvinskelvins

T (K) = t (˚C) + 273.15T (K) = t (˚C) + 273.15Body temp = 37 ˚C + 273 = 310 KBody temp = 37 ˚C + 273 = 310 K

Liquid nitrogen = -196 ˚C + 273 = 77 KLiquid nitrogen = -196 ˚C + 273 = 77 K

Dimensional Dimensional AnalysisAnalysis

Conversion FactorsConversion Factors

Fractions in which the numerator and denominator are EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

How many minutes are in 2.5 hoursHow many minutes are in 2.5 hours??

Conversion factor

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min 1 hr1 hr

cancel

By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up,

and the UNITS are calculated as well as the numbers!

English and Metric English and Metric ConversionsConversions

If you know ONE conversion for each type of measurement, you can convert anything!

You will need to know and use these conversions:◦Mass: 454 grams = 1 pound◦Length: 2.54 cm = 1 inch◦Volume: 0.946 L = 1 quart

Steps to Problem SolvingSteps to Problem Solving

1. Read problem2. Identify data 3. Make a unit plan from the initial unit to

the desired unit4. Select conversion factors5. Change initial unit to desired unit6. Cancel units and check7. Do math on calculator 8. Give an answer using significant figures

Simplified Problem Solving Simplified Problem Solving StrategyStrategy

Where do we want to go?

What do we know?

How do we get there?

Does it make sense?