SI System andUnit Conversions

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What makes a measurement useful?

• It must include a number and a unit.• A standard must be used– An exact quantity that people agree to use for

comparison.

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SI System

• Scientists use SI system– International System of Units– SI comes from the French • “Systeme International d’Unites”

– revised version of the metric system

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SI Standard UnitsQuantity Standard Unit Symbol

Length meter m

Mass kilogram kg

Temperature Kelvin K

Time second s

Amount of substance mole mol

Electric Current ampere (amp) A

Luminous Intensity candela cd

The SI system is built on these 7 units, each of which have a standard. All other SI units can be derived from these.

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Derived SI units

• Any combination of SI units such as– g/cm3

– m/s2

– Newton (N)

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Common SI derived unitsQuantity Unit symbol

Area Square meter m2

Volume Cubic meter m3

Density Kilograms per cubic meter kg/m3

Pressure Pascal (kilogram per meter second squared)

Pa (kg/m•s2)

Energy Joule J (kg•m2/s2 )

Force Newton N (kg•m/s2)

Frequency Hertz (cycles per second, reciprocal second))

Hz (1/s or s-1)

Electric charge Coulomb (ampere second) C (A•s)

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Non SI units commonly used in scienceQuantity Unit Useful

relationshipsExample

Volume Liter (L) 1L=1000cm3

1mL=1cm31L approximately equals a quart1mL≈ 20 drops H2O

Energy calorie (cal) 1cal=4.184J1J=0.2390cal

Amount of heat that raises the temperature of 1g of H2O by 1◦C

Temperature Celsius, CFahrenheit, F

K=◦C + 273◦C=5/9 (◦F - 32)◦F=9/5◦C +32

Water freezes at 273K, 0◦C, and 32◦FWater boils at 373K, 100◦C, and 212◦F

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Prefixes

• Base units are not always convenient– For very large or very small values

• Represent measurements in a more compact way with the use of prefixes

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• Example– The time it takes for a computer hard drive to read

or write data might be 0.009 seconds. – We can more conveniently represent this time as 9

milliseconds, where the prefix “milli” means “thousandth” • So 9 milliseconds means 9 thousandths of a second, or

0.009 seconds

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SI PrefixesPrefix Symbol Meaning

giga- G Billion (109)

mega- M Million (106)

kilo- K Thousand (103)

hecto- H Hundred (102)

deka- da Ten (101)

deci- d Tenth (10-1)

centi- c Hundredth (10-2)

milli- m Thousandth (10-3)

micro- μ Millionth (10-6)

nano- n Billionth (10-9)

pico- p Trillionth (10-12)

femto- f (10-15)

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Examples to remember: lengthUnit Example

Kilometer (km) Length of about 5 city blocks

Meter Height of doorknob from floor

Decimeter Diameter of a large orange

Centimeter Width of a shirt button

Millimeter Thickness of a dime

Micrometer Diameter of a bacterial cell

Nanometer Thickness of an RNA molecule

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Examples to remember: volumeUnit Example

Liter (L) Quart of milk

Milliliter (mL) About 20 drops of water

Cubic centimeter (cm3) Cube of sugar

Microliter (μL) Crystal of table salt

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Examples to remember: massUnit Example

Kilogram (kg) Small textbook

Gram (g) Dollar bill or paper clip

Milligram (mg) Ten grains of salt

Microgram (μg) Particle of baking powder

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Converting SI units

• The SI system is based on powers of 10 – units can be converted by simply moving the

decimal

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King Henry’s Daughter Barbara Drinks Chocolate Milk

kilo hecto deka Base deci centi milli

(No prefix)

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To convert a unit by moving the decimal…

1. Find the prefix of the given measurement on the chart2. Count over to the right or left to reach the desired unit3. Move the decimal the same direction and same number of places

Example: Convert 360 g to mg4. Start at the base unit grams5. Count over 3 steps to the right to reach milli-6. Move the decimal 3 places to the right

360.000 so 360,000mg

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• Example45.2cg = _____kg1. Start at the prefix centi-2. Count over 5 steps to the left to reach kilo-3. Move the decimal 5 places to the left00045.2 so 0.000452kg

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Temperature

• Related to the average kinetic energy of the particles in a sample of matter

• a physical property that determines the direction of heat flow

• Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature

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Temperature Conversions

• Three temperature scales– Fahrenheit (⁰F)

• U.S. commonly uses (weather, oven temperatures, etc)– Celsius (⁰C)

• Most other countries commonly use• This is the scale we use in lab

– Kelvin (K)• “absolute” temperature scale• O Kelvin is called absolute zero- the lowest possible

temperature when molecular motion ceases, particles have no kinetic energy

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Temperature Scale

Water Freezes at

Water Boils at Body Temperature

Absolute Zero

Fahrenheit 32◦F 212◦F 98.6◦F -460◦FCelsius 0◦C 100◦C 37◦C -273◦CKelvin 273 K 373 K 310 K O K

Note that the degree symbol is not used with the Kelvin scale. When reading a Kelvin temperature, the correct way is to say “273 Kelvin” instead of “273 degrees Kelvin”.

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Temperature conversions

• Use the following equations to convert from one temperature scale to another.

Conversion FormulaCelsius to Kelvin K = C + 273Kelvin to Celsius C= K - 273Fahrenheit to Celsius C = (F – 32) x 5/9Celsius to Fahrenheit F = (C x 9/5) + 32

*To convert between Kelvin and Fahrenheit is a two step process. Convert to Celsius first, then to Kelvin or Fahrenheit.

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English Units

• Most of us in the U.S. grow up using English units such as pounds and inches.

• To convert between English units or between English and metric units, you must use a method called dimensional analysis.

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Dimensional Analysis

• Equality statements such as 1ft=12in. are made into fractions and then strung together in such a way that all units except the desired one are canceled out of the problem

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• Keeping track of units can help you – convert one measured quantity into its equivalent

quantity of a different unit– Set up a calculation without the need for a

formula

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To set up a conversion problem…

1. write down all “=“ statements you know that will help you get from the given unit to the new unit– Look for equalities given in the problem

• ExampleHow many inches are in 1.25 miles? (There are 5,280ft in

1mile.)“=“ statements: Given: 5,280ft=1mileOther: 12in=1ft

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2. Make fractions out of your “=“ statements. There are 2 fractions for each “=“ that are reciprocals of each other. These fractions are called “conversion factors”

• Example5,280ft=1mile 5,280ft or 1mile

1mile 5,280ft

12in.=1ft 12in or 1ft 1ft 12in

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3. Begin solving the problem by writing the given amount with units on the left side of your paper then choose the fractions that will let a numerator unit be canceled with a denominator unit and vice versa until all units are canceled except the desired unit

Example1.25miles x 5,280ft x 12in =_______in 1mile 1ft

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4. Using your calculator, read from left to right and enter the numerator and denominator numbers in order. Precede each numerator with a multiplication sign and each denominator with a division sign.

Example1.25miles x 5,280ft x 12in =_______in 1mile 1ft

On your calculator: 1.25x5280/1x12/1=

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5. Round your calculated answer to the same number of significant digits your original given number had. (conversion factors are exact numbers and so don’t affect the number of sig. digits)

Example1.25miles x 5,280ft x 12in = 79,200 in 1mile 1ft

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example

• Suppose your automobile tank holds 23 gallons and the price of gasoline is 33.5¢ per liter. How many dollars will it cost you to fill your tank?

• From the problem, 33.5¢ = 1L• From a reference table, 1L=1.06qt

4qt=1gal

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More complex problems…

• Measurements may contain – More than one unit, such as miles/hr– fractional or exponential units such as cm3

• treat each unit independently• Structure your conversion factors to ensure the given

units cancel with a numerator or denominator as appropriate and the answer ends with the appropriate unit

• Remember information given in the problem can be an equality

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• A car is traveling down the interstate at a speed of 70 miles per hour (70miles/1hr). Convert this speed to m/s.

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Squared and cubed units

• Squared and cubed units are potentially tricky• For example, remember that a cm3 is really a

cm x cm x cm• If we were going to convert cm3 to mm3 – We need to use the conversion factor 1cm=10mm

three times (or cube it) so that all three centimeter units cancel out

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• One liter is exactly 1000cm3. How many cubic inches are there in 1.0L?

• 1000cm3=1L• 1in=2.54cm