si system and unit conversions
DESCRIPTION
SI System and Unit Conversions. 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. . SI System. Scientists use SI system International System of Units SI comes from the French - PowerPoint PPT PresentationTRANSCRIPT
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