2.6 SI Units

2.6 SI Units2.6 SI Units The International System of Units, SI, is The International System of Units, SI, is

a revised version of the metric systema revised version of the metric system Correct units along with numerical Correct units along with numerical

values are critical when communicating values are critical when communicating measurements.measurements.

The are seven base SI units (Table 2.1) The are seven base SI units (Table 2.1) of which other SI units are derived.of which other SI units are derived. Sometimes non-SI units are preferred for Sometimes non-SI units are preferred for

convenience or practical reasonsconvenience or practical reasons

2.6 SI Units – Table 2.22.6 SI Units – Table 2.2QuantityQuantity SI Base or Derived SI Base or Derived

UnitUnitNon-SI UnitNon-SI Unit

LengthLength meter (m)meter (m)VolumeVolume cubic meter (mcubic meter (m33)) literliterMassMass kilogram (kg)kilogram (kg)DensityDensity grams per cubic grams per cubic

centimeter (g/cmcentimeter (g/cm33); ); grams per mililiter grams per mililiter (g/mL)(g/mL)

TemperatTemperatureure

kelvin (K)kelvin (K) degree Celcius (°C) degree Celcius (°C)

TimeTime second (s)second (s)PressurePressure Pascal (Pa)Pascal (Pa) atmosphere (atm); atmosphere (atm);

milimeter of mercury milimeter of mercury (mm Hg)(mm Hg)

EnergyEnergy joule (J)joule (J) calorie (cal)calorie (cal)

Common SI Prefixes Common SI Prefixes Units larger than the base unitUnits larger than the base unitTeraTera TT ee1212 base base

unitsunitstermeter (Tm)termeter (Tm)

GigaGiga GG ee9 9 base base unitsunits

gigameter gigameter (Gm)(Gm)

MegaMega MM ee6 6 base base unitsunits

megameter megameter (Mm)(Mm)

KiloKilo kk ee3 3 base base unitsunits

kilometer kilometer (km)(km)

HectoHecto hh ee2 2 base base unitsunits

hectometer hectometer (hm)(hm)

DekaDeka dada ee1 1 base base unitsunits

decameter decameter (dam)(dam)

Base Base UnitUnit

ee0 0 base base unitsunits

meter (m)meter (m)

Common SI PrefixesCommon SI Prefixes Units smaller than the base unit Units smaller than the base unit Base Base UnitUnit

ee0 0 base base unitsunits

meter (m)meter (m)

DeciDeci dd ee-1 -1 base base unitsunits

decimeter decimeter (dm)(dm)

CentiCenti cc ee-2 -2 base base unitsunits

centimeter centimeter (cm)(cm)

MilliMilli mm ee-3 -3 base base unitsunits

millimeter millimeter (mm)(mm)

MicroMicro μμ ee-6 -6 base base unitsunits

micrometer micrometer ((μμm)m)

NanoNano nn ee-9 -9 base base unitsunits

Nanometer Nanometer (nm)(nm)

PicoPico pp ee-12 -12 base base unitsunits

picometer picometer (pm)(pm)

Common SI PrefixesCommon SI Prefixes A mnemonic device can be used to A mnemonic device can be used to

memorize these common prefixes in memorize these common prefixes in the correct order:the correct order: TThe he GGreat reat MMonarch onarch KKing ing HHenry enry DDied ied

BBy y DDrinking rinking CChocolate hocolate MMocha ocha MMilk ilk NNot ot PPilsnerilsner

2.7 Units of Length2.7 Units of Length The basic unit of length is the The basic unit of length is the metermeter Prefixes can be used with the base Prefixes can be used with the base

unit to more easily represent small or unit to more easily represent small or large measurementslarge measurements Example: A hyphen (12 point font) Example: A hyphen (12 point font)

measures about 0.001 m or 1 mm.measures about 0.001 m or 1 mm. Example: A marathon race is Example: A marathon race is

approximately approximately 42,000 m or 42 km.42,000 m or 42 km.

2.7 Concept Practice2.7 Concept Practice15. Use the tables in the text to order 15. Use the tables in the text to order

these lengths from smallest to these lengths from smallest to largest.largest.a. centimetera. centimeterb. micrometerb. micrometerc. kilometerc. kilometerd. millimeterd. millimetere. metere. meterf. decimeterf. decimeter

- 1 (smallest)- 1 (smallest)

- 2- 2

- 3- 3

- 4- 4- 5- 5

- 6 (largest)- 6 (largest)

2.8 Units of Volume2.8 Units of Volume The space occupied by any sample of The space occupied by any sample of

matter is called its matter is called its volumevolume The volume ofThe volume of rectangular solids rectangular solids can can

be calculated by multiplying the be calculated by multiplying the lengthlength by by widthwidth by by heightheight Units are cubed because you are measuring Units are cubed because you are measuring

in 3 dimensionsin 3 dimensions Volume ofVolume of liquids liquids can be measured can be measured

with a with a graduated cylindergraduated cylinder, a , a pipetpipet, a , a buretburet, or a , or a volumetric flaskvolumetric flask

2.8 Units of Volume2.8 Units of Volume A convenient unit of measurement for A convenient unit of measurement for

volume in everyday use is the liter (L)volume in everyday use is the liter (L) Milliliters (mL) are commonly used for Milliliters (mL) are commonly used for

smaller volume measurements and smaller volume measurements and liters (L) for larger measurementsliters (L) for larger measurements 1 mL = 1 cm1 mL = 1 cm33

10 cm x 10 cm x 10 cm = 1000 cm10 cm x 10 cm x 10 cm = 1000 cm33 = 1 L = 1 L

2.8 Units of Volume2.8 Units of Volume

2.8 Concept Practice2.8 Concept Practice17. From what unit is a measure of 17. From what unit is a measure of

volume derived?volume derived?A: Volume is a length measurement A: Volume is a length measurement

cubed.cubed.

2.8 Practice2.8 Practice18. What is the volume of a paperback 18. What is the volume of a paperback

book 21 cm tall, 12 cm wide, and 3.5 cm book 21 cm tall, 12 cm wide, and 3.5 cm thick?thick?

A: 882 cmA: 882 cm33 → → 880 cm880 cm33; ; 8.8 x 108.8 x 102 2 cmcm33

19. What is the volume of a glass cylinder 19. What is the volume of a glass cylinder with an inside diameter of 6.0 cm and a with an inside diameter of 6.0 cm and a height of 28 cm?height of 28 cm?V=V=ππrr22hh

A: A: 790 cm790 cm33; ; 7.9 x 107.9 x 102 2 cmcm33

2.9 Units of Mass2.9 Units of Mass A person on the moon would weigh 1/6 of A person on the moon would weigh 1/6 of

his/her weight on Earth.his/her weight on Earth. This is because the force of gravity on the This is because the force of gravity on the

moon is approximately 1/6 of its force of Earth.moon is approximately 1/6 of its force of Earth. Weight is a forceWeight is a force – it is a measure of the pull – it is a measure of the pull

on a given mass by gravity; it can change by on a given mass by gravity; it can change by location.location.

Mass is the quantity of matter an Mass is the quantity of matter an object containsobject contains Mass remains constant regardless of location.Mass remains constant regardless of location.

Mass v. WeightMass v. Weight

http://videos.howstuffworks.com/hsw/9935-exploring-gravity-mass-and-weight-video.htm

2.9 Units of Mass2.9 Units of Mass The The kilogramkilogram is the basic SI unit of is the basic SI unit of

massmass It is defined as the mass of 1 L of water It is defined as the mass of 1 L of water

at 4°C.at 4°C. A gram, which is a more commonly A gram, which is a more commonly

used unit of mass, is 1/1000 of a used unit of mass, is 1/1000 of a kilogramkilogram 1 gram = the mass of 1 cm1 gram = the mass of 1 cm33 of water at of water at

4°C.4°C.

2.9 Concept Practice2.9 Concept Practice20. As you climbed a mountain and the force 20. As you climbed a mountain and the force

of gravity decreased, would your weight of gravity decreased, would your weight increase, decrease, or remain constant? increase, decrease, or remain constant? How would your mass change? Explain.How would your mass change? Explain.

A: Your weight would decrease; mass would A: Your weight would decrease; mass would remain constant.remain constant.

21. How many grams are in each of these 21. How many grams are in each of these quantities?quantities?a. 1 cga. 1 cg b. 1 b. 1 μμgg c. 1 kgc. 1 kg d. 1mgd. 1mg

A: 0.01g 0.000001g 1000g 0.001 gA: 0.01g 0.000001g 1000g 0.001 g

2.10 Density2.10 Density DensityDensity is the ratio of the is the ratio of the massmass of an of an

object to its object to its volumevolume.. Equation →Equation → D = mass/volumeD = mass/volume

Common units: g/cmCommon units: g/cm33 or g/mL or g/mL Example: 10.0 cmExample: 10.0 cm33 of lead has a mass of lead has a mass

114 g114 g Density (of lead) = 114 g / 10.0 cmDensity (of lead) = 114 g / 10.0 cm33 = = 11.4 g/cm11.4 g/cm33

See Table 2.7, page 46See Table 2.7, page 46

2.10 Density2.10 Density Density determines if an object will Density determines if an object will

float in a fluid substance.float in a fluid substance. Examples: Ice in water; hot air risesExamples: Ice in water; hot air rises

Density can be used to identify Density can be used to identify substancessubstances See Table 2.8, page 46See Table 2.8, page 46

2.10 Concept Practice2.10 Concept Practice22. The density of silver is 10.5 g/cm22. The density of silver is 10.5 g/cm33

at 20°C. What happens to the at 20°C. What happens to the density of a 68-g bar of silver that is density of a 68-g bar of silver that is cut in half?cut in half?A: Its density does not change.A: Its density does not change.

2.10 Concept Practice2.10 Concept Practice23. A student finds a shiny piece of metal 23. A student finds a shiny piece of metal

that she thinks is aluminum. In the lab, that she thinks is aluminum. In the lab, she determines that the metal has a she determines that the metal has a volume of 245 cmvolume of 245 cm33 and a mass of 612 g. Is and a mass of 612 g. Is the metal aluminum?the metal aluminum?A: Density = 2.50 g/cmA: Density = 2.50 g/cm33; the metal is not ; the metal is not aluminum.aluminum.

24. A plastic ball with a volume of 19.7 cm24. A plastic ball with a volume of 19.7 cm33 has a mass of 15.8 g. Would this ball sink has a mass of 15.8 g. Would this ball sink or float in a container of gasoline?or float in a container of gasoline?A: Density = 0.802 g/cmA: Density = 0.802 g/cm33; the ball will ; the ball will sink.sink.

2.10 Specific Gravity 2.10 Specific Gravity (Relative Density)(Relative Density)

Specific gravitySpecific gravity is a comparison of the is a comparison of the density of a substance to the density of a density of a substance to the density of a reference substance, usually at the same reference substance, usually at the same temperature.temperature. Water at 4°C, which has a density of 1 g/cm3, Water at 4°C, which has a density of 1 g/cm3,

is commonly used as a reference substance.is commonly used as a reference substance.Specific gravity = Specific gravity = density of substance (g/cm3)density of substance (g/cm3)

density of water (g/cm3)density of water (g/cm3) Because units cancel, a measurement of Because units cancel, a measurement of

specific gravity has no unitsspecific gravity has no units A hydrometer can be used to measure the A hydrometer can be used to measure the

specific gravity of a liquid.specific gravity of a liquid.

2.11 Concept Practice2.11 Concept Practice25. Why doesn’t a measurement of specific 25. Why doesn’t a measurement of specific

gravity have a unit?gravity have a unit?A: Because it is a ratio of two density A: Because it is a ratio of two density measurements, the density units cancel out.measurements, the density units cancel out.

26. Use the values in Table 2.8 to calculate 26. Use the values in Table 2.8 to calculate the specific gravity of the following the specific gravity of the following substances.substances.a. Aluminuma. Aluminum b. Mercuryb. Mercury c. icec. ice

A: 2.70A: 2.70 13.6 13.6 0.917 0.917

2.12 Measuring 2.12 Measuring TemperatureTemperature

Temperature determines the direction of Temperature determines the direction of heat transfer between two objects in heat transfer between two objects in contact with each other.contact with each other. Heat moves from the object at the Heat moves from the object at the higher higher

temperaturetemperature to the object at a to the object at a lower lower temperature.temperature.

TemperatureTemperature is a measure of is a measure of the degree the degree of hotness or coldness of an objectof hotness or coldness of an object..

Almost all substances expand with an Almost all substances expand with an increase in temperature and contract with increase in temperature and contract with a decrease in temperaturea decrease in temperature An important exception is waterAn important exception is water


There are various temperature There are various temperature scalesscales

On the On the CelsiusCelsius temperature scale temperature scale the the freezing point of water is freezing point of water is taken as 0°Ctaken as 0°C and the and the boiling point boiling point of water at 100°Cof water at 100°C


The The Kelvin scaleKelvin scale (or absolute scale) is (or absolute scale) is another temperature scale that is usedanother temperature scale that is used On the Kelvin scale the freezing point of On the Kelvin scale the freezing point of

water is water is 273 K273 K and the boiling point is and the boiling point is 373 K373 K

(degrees are not used).(degrees are not used). 1°C = 1 Kelvin1°C = 1 Kelvin The zero point (0 K) on the Kelvin scale is The zero point (0 K) on the Kelvin scale is

called called absolute zeroabsolute zero and is equal to -273°C and is equal to -273°C Absolute zero is where all molecular motion stopsAbsolute zero is where all molecular motion stops


Converting Temperatures:Converting Temperatures: K = °C + 273K = °C + 273 °C = K - 273°C = K - 273

2.12 Concept Practice2.12 Concept Practice27. Surgical Instruments may be 27. Surgical Instruments may be

sterilized by heating at 170°C for 1.5 sterilized by heating at 170°C for 1.5 hours. Convert 170°C to kelvins.hours. Convert 170°C to kelvins.A: K = 170°C + 273 = 443 KA: K = 170°C + 273 = 443 K

28. The boiling point of the element 28. The boiling point of the element argon is 87 K. What is the boiling argon is 87 K. What is the boiling point of argon in °C?point of argon in °C?A: °C = 87 K – 273 = -186°CA: °C = 87 K – 273 = -186°C

2.13 Evaluating 2.13 Evaluating MeasurementsMeasurements

Accuracy in measurement depends on the Accuracy in measurement depends on the quality of the measuring instrumentquality of the measuring instrument and the and the skill of the person using the skill of the person using the instrumentinstrument.. Errors in measurement could have various Errors in measurement could have various

causescauses In order to evaluate the accuracy of a In order to evaluate the accuracy of a

measurement, you must be able to measurement, you must be able to compare it to the true or compare it to the true or accepted accepted valuevalue..


accepted valueaccepted value – the true or correct – the true or correct value based or reliable referencesvalue based or reliable references

experimental valueexperimental value – the measured – the measured value determined in the experimentvalue determined in the experiment

The difference between the The difference between the accepted accepted valuevalue and the and the experimental valueexperimental value is is the the errorerror.. error = accepted value – experimental error = accepted value – experimental

valuevalue


The The percent errorpercent error is the is the errorerror divided divided by the by the accepted valueaccepted value, expressed as a , expressed as a percentage of the accepted value.percentage of the accepted value.Percent Error =Percent Error = x 100 x 100

An error can be positive or negative, An error can be positive or negative, but an absolute value of error is used but an absolute value of error is used so that the percentage is positiveso that the percentage is positive

|error||error| AVAV

2.13 Concept Practice2.13 Concept Practice32. A student estimated the volume of a 32. A student estimated the volume of a

liquid in a beaker as 200 mL. When liquid in a beaker as 200 mL. When she poured the liquid into a graduated she poured the liquid into a graduated cylinder she measured the value as cylinder she measured the value as 200 mL. What is the percent error of 200 mL. What is the percent error of the estimated volume from the beaker, the estimated volume from the beaker, taking the graduated cylinder taking the graduated cylinder measurement as the accepted value?measurement as the accepted value?A: A: Percent Error =Percent Error = x 100 = 4%x 100 = 4%

|200 mL - 208 mL||200 mL - 208 mL|200 mL200 mL

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2.6 SI Units