11

SI and Metric BasicsSI and Metric BasicsChapter 1Chapter 1

Includes SI units, first lab Includes SI units, first lab equipment, and unit equipment, and unit

conversionconversion

22

The 7 SI UnitsThe 7 SI Units

QuantityQuantity UnitUnit

Length (Length (ll)) Meter (m)Meter (m)

Mass (Mass (mm)) Kilogram (kg)Kilogram (kg)

Time (Time (tt)) Second (s)Second (s)

Temperature (Temperature (TTxx)) Kelvin (K)Kelvin (K)

Electric current (Electric current (II)) Ampere (A)Ampere (A)

Amount of substance (Amount of substance (nn)) Mole (mol)Mole (mol)

Luminous intensity (?)Luminous intensity (?) Candela (cd)Candela (cd)

33

Derived unitsDerived units

Units that are combinations of the Units that are combinations of the base units by multiplication or base units by multiplication or division.division.

What to look for:What to look for:– Units that are fractions (m/s or g/cmUnits that are fractions (m/s or g/cm33),),– Units that are products (N*m)Units that are products (N*m)– Units that have powers (cmUnits that have powers (cm33),),– Units other than the 7 SI units.Units other than the 7 SI units.

44

Multiplied or divided unitsMultiplied or divided units

Treat units as variables: Treat units as variables: 1.1. (m)(m) = m(m)(m) = m22

2.2. (mol)(mol)(mol) = (mol)(mol)(mol)(mol) = (mol)33

3.3. ss22/s = s/s = s

4.4. mm33/m = m/m = m22

5.5. 3m + 6m = 9m3m + 6m = 9m

6.6. (x)(x) = x(x)(x) = x22

Which of these examples does not show Which of these examples does not show the making of a “derived unit”?the making of a “derived unit”?

55

4 Common Prefixes4 Common Prefixes

PrefixPrefix SymbolSymbol MeaningMeaning Multiplies base unit Multiplies base unit by…by…

MegaMega MM MillionMillion 1,000,0001,000,000

KiloKilo kk ThousandThousand 1,0001,000

CentiCenti cc HundredthHundredth 0.010.01

MilliMilli mm ThousandthThousandth 0.0010.001

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The 7 SI UnitsThe 7 SI Units

QuantityQuantity UnitUnit

Length (Length (ll)) Meter (m)Meter (m)

Mass (Mass (mm)) Kilogram (kg)Kilogram (kg)

Time (Time (tt)) Second (s)Second (s)

Temperature (Temperature (TTxx)) Kelvin (K)Kelvin (K)

Electric current (Electric current (II)) Ampere (A)Ampere (A)

Amount of substance (Amount of substance (nn)) Mole (mol)Mole (mol)

Luminous intensity (?)Luminous intensity (?) Candela (cd)Candela (cd)

Take a moment to notice here that the “official SI unit” for mass is not a plain base unit. It is grams with the prefix kilo attached, meaning “1,000 grams”!

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Wal-Mart ObservationsWal-Mart Observations

Solids in bottles are usually Solids in bottles are usually measured in grams or kilograms measured in grams or kilograms (that’s mass).(that’s mass).

Liquids in bottles are usually Liquids in bottles are usually measured in milliliters or liters (that’s measured in milliliters or liters (that’s volume).volume).

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Prefix powers of 10Prefix powers of 10

Mega is 10Mega is 1066 (1,000,000) (1,000,000) Kilo is 10Kilo is 1033 (1,000) (1,000) Centi is 10Centi is 10-2-2 (0.01) (0.01) Milli is 10Milli is 10-3-3 (0.001) (0.001) Do you notice any pattern here?Do you notice any pattern here? These can be used in metric These can be used in metric

conversions.conversions.

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““Powers for Prefixes” Metric Powers for Prefixes” Metric ConversionConversion

Replace a unit prefix with its power Replace a unit prefix with its power of ten.of ten.

Multiply number of units by power of Multiply number of units by power of 10.10.

Write new number and a unit with no Write new number and a unit with no prefix.prefix.

Practice until you are a master of Practice until you are a master of substituting powers for prefixessubstituting powers for prefixes

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Power for Prefix ExamplePower for Prefix Example

Given: 17 kg = Given: 17 kg = ? ? g g Known: Known:

kgkg means means kilogramkilogram

KiloKilo means 10 means 1033

17 kg = 17 (1017 kg = 17 (1033) grams) grams 17 (1017 (1033) grams = 17,000 grams) grams = 17,000 grams

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Metric Conversion StairwayMetric Conversion Stairway

To change a number with a prefix To change a number with a prefix (such as 15 (such as 15 cm)cm) to a number to a number without a prefix (such as without a prefix (such as m), m), do the do the following:following:

1.1. Remember that all you are just Remember that all you are just switching decimal places.switching decimal places.

2.2. Think about which units are larger Think about which units are larger and which ones are smaller.and which ones are smaller.

3.3. Use the following chartUse the following chart

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Metric Conversion StairwayMetric Conversion Stairway

mm

cc

dd

bb

dada

hh

kkkilo

basic

centi milli

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Using the Stairway exampleUsing the Stairway example

Given: 15 cmGiven: 15 cm Desired unit: meterDesired unit: meter Meter has no prefix, so we consider it Meter has no prefix, so we consider it

basicbasic.. From the From the centicenti step, note how many step, note how many

steps it is to the steps it is to the basic stepbasic step.. It is two steps to the left.It is two steps to the left. Move the decimal two places to the Move the decimal two places to the

left to convert 15 cm to left to convert 15 cm to 0.15 m0.15 m..

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Stairway ObservationsStairway Observations

Moving from right to left, the answer Moving from right to left, the answer will be a smaller number than the will be a smaller number than the given.given.

Moving from Left to Right, the Moving from Left to Right, the answer will be a larger number than answer will be a larger number than the given.the given.

The two numbers’ units make the The two numbers’ units make the values equivalent.values equivalent.

There are seven steps on the There are seven steps on the stairway. Others could be added.stairway. Others could be added.

1515

Finding DensityFinding Density

If you know both the mass and the If you know both the mass and the volume of an object, you can find the volume of an object, you can find the density of the object.density of the object.

Here’s how:Here’s how:Divide the mass by the volume.Divide the mass by the volume.

Try the example on the next slide.Try the example on the next slide.

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Density ExampleDensity Example

Given:Given:Mass of object = 2,000 gMass of object = 2,000 g

Volume of object = 140 cmVolume of object = 140 cm33

Formula: Formula: D = m / VD = m / V Numbers in the formula:Numbers in the formula:

D = 2,000 g / 140 cmD = 2,000 g / 140 cm33

Answer: 14.3 g/cmAnswer: 14.3 g/cm33

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Finding AgeFinding Age

To find your age in metric units, we To find your age in metric units, we will have to convert years to will have to convert years to seconds. Here’s how:seconds. Here’s how:– Turn years to days (365.25 days per yr)Turn years to days (365.25 days per yr)– Turn days to hours (24 hr per day)Turn days to hours (24 hr per day)– Turn hours to minutes (60 min per hr),Turn hours to minutes (60 min per hr),– Turn minutes to seconds (60 sec per Turn minutes to seconds (60 sec per

min)min)

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Age ExampleAge Example

Try converting 16 years to seconds.Try converting 16 years to seconds.16 yr (365.25 days / yr) = 5,844 days16 yr (365.25 days / yr) = 5,844 days

5,844 days (24 hr / day) = 140,256 hr5,844 days (24 hr / day) = 140,256 hr

140,256 hr (60 min / hr) = 8,415,360 min140,256 hr (60 min / hr) = 8,415,360 min

8,415,360 min (60 sec / min) = 8,415,360 min (60 sec / min) = drumrolllllldrumrollllll

504,921,600 sec504,921,600 sec

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Factor LabelsFactor Labels

In the example we just used, each In the example we just used, each number was labeled with a unit.number was labeled with a unit.

Mathematically, the units are Mathematically, the units are changed in each stepchanged in each step– From years to days to hours to minutes From years to days to hours to minutes

to seconds.to seconds.– One unit is cancelled out in each step One unit is cancelled out in each step

until the desired unit is reached.until the desired unit is reached.

2020

Turning Pounds into KilogramsTurning Pounds into Kilograms

If you ever travel internationally, it If you ever travel internationally, it may be useful to know your weight in may be useful to know your weight in SI units. Here’s how to do it:SI units. Here’s how to do it:– Remember that there are 2.2 lbs per Remember that there are 2.2 lbs per

kilogram.kilogram.– Take your weight and divide it by Take your weight and divide it by 2.2 lbs 2.2 lbs

/ 1 kg/ 1 kg.. Let’s try an example.Let’s try an example.

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Pounds to kilograms examplePounds to kilograms example

Given: A man weighs 215 lbs.Given: A man weighs 215 lbs. Conversion factor: 2.2 lbs / kgConversion factor: 2.2 lbs / kg Divide: 215 lbs / (2.2 lbs / kg) = Divide: 215 lbs / (2.2 lbs / kg) =

Answer: 97.7 kgAnswer: 97.7 kg Notice the unit Notice the unit kg kg is the only one left. is the only one left.

The The lbs lbs units have cancelled out.units have cancelled out.

2222

First Lab EquipmentFirst Lab Equipment

We will be using the following pieces We will be using the following pieces of special lab equipment in our first of special lab equipment in our first lab.lab.– BeakerBeaker– Graduated cylinder Graduated cylinder – Temperature probeTemperature probe– TI-84 Graphing CalculatorTI-84 Graphing Calculator

2323

BeakerBeaker

A cup marked for A cup marked for approximate liquid approximate liquid measurements.measurements.

Not very accurate Not very accurate measurements.measurements.

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Graduated CylinderGraduated Cylinder

Cylinder marked Cylinder marked with lines for with lines for measuring liquid measuring liquid volumes volumes accurately.accurately.

Sometimes used in Sometimes used in finding solid finding solid volumes dropped volumes dropped into the liquid.into the liquid.

2525

Temperature ProbeTemperature Probe

A stainless steel A stainless steel thermometer used thermometer used with the TI-84 with the TI-84 graphing calculatorgraphing calculator

An An EZ-linkEZ-link is used is used to connect the to connect the probe to the probe to the calculator.calculator.