Units of Measurement : SI unit and derived units
Unit prefixes
Unit conversion using dimensional analysis
Scientific notation
Increment, Accuracy, Precision
MEASUREMENT
Distinguish between a number and a quantity.
Name SI units for length, mass, time, temperature, volume and density.
Define and identify base units; unit conversions; identify prefixes
Perform unit conversion using dimensional analysis.
OBJECTIVES OBJECTIVES
Units of MeasurementUnits of Measurement•In our daily lives we deal with making measurements routinely.
–i.e., How much gasoline is required to fill your gas tank? What time did you wake up this morning? How fast did you drive to school today ?
•Doctors, nurses, pharmacists-–Doctors and nurses make measurements constantly. Measurements like pulse rate, blood pressure, temperature, drug dosage.
•Math - The language of Science–Scientists make countless measurements during their experiments to prove or disprove a theory.
Units of MeasurementUnits of Measurement
What is your response if I told you that:
I weigh 65
In any measurement magnitude (the number)
as well as the unit (meaning) must be stated.
Otherwise, it is meaningless!
Number vs. Quantity• Quantity : number + unit
UNITS MATTER!!
Systems of MeasurementScientific Scientific
CommunityCommunityScientific Scientific
CommunityCommunityThe Rest of the The Rest of the WorldWorld
AmericaAmerica
English SystemEnglish System1 ft = 12 in1 yd= 3 ft1 mi. = 1,760 Yd1 mi = 5280 ft
Metric SystemMetric System1 km = 1000 m1 m = 100 cm
Le SystemLe SystemInternational d’UnitesInternational d’UnitesLe SystemLe SystemInternational d’UnitesInternational d’Unites
What units are used?What units are used?
SI Units are basically an updated form of the metric system.
Metric system and theMetric system and theLe Systeme International d'Unites (SI)Le Systeme International d'Unites (SI)
• The Metric system is convenient because it uses only one fundamental unit for each type of measurement. For example for:
*Length we use only meter, in the US we use foot, yard, inch.
*Mass we use Kg not pound.
• All the Prefixes are multiples of 10.
SI Units
Quantity Base Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
m
kg
s
K
Amount of particles mole mol
Symbol
l
m
t
T
n
SI Prefix Conversions
Giga
Mega-
G 109
deci- d 10-1
centi- ?
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
BASE UNIT --- 1
kilo- k 103
Hecto- h 102
Deka- da 10
106
Derived Units: Combination of base units
• Area ( m2)• length length = m x m
• Volume (m3) – length length length= m x m x m
D = MV
• Density (g/cm3)– mass per volume
Temperature
A measure of how hot or how cold an object is.
SI Unit: the kelvin ( K )
• Note: not a degree
• Absolute Zero= 0 K
Temperature Scales
Celsius and Kelvin
K= oC + 273
Density• An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 g
V
MD
Density• A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
WORK:
V = M D
V = 25 g
0.87 g/mL
V = 29 mLV
MD
Unit conversion using dimensional
analysis
Page
Unit 1 - MEASUREMENT
SI Prefix Conversions
1. Find the difference between the
exponents of the two prefixes.
2. Move the decimal that many places.
To the leftor right?
SI Prefix Conversions
mo
ve l
eft
mo
ve r
igh
t
Giga
Mega-
G 109
deci- d 10-1
centi- ?
milli- m 10-3
Prefix Symbol Factor
micro- 10-6
BASE UNIT --- 1
kilo- k 103
Hecto- H 102
Deca- D 10
106
SI Prefix Conversions
1) 20 cm = ___________ m
2) 0.032 L = ______________ mL
3) 45 m = ______________ cm
4) 80.5 km = ______________ m
How would you convert 2h 45 min to second
Convert 55.00 km/h to m/s
• Steps:
1. Identify starting ( also called given, old )&
ending ( target, new) units.
2. Line up conversion factors so units cancel.( hint : the new units should on the top)
3. Multiply all top numbers & divide by each bottom number. ( )
4. Check units & answer.
Converting by using Dimensional Analysis
Identify
10.0 in
We start by writing down the Given (old) and its Unit
Converting by using Dimensional Analysis: inch to cm
Line up
10.0 in x
1 in
2.54 cm
We know 1 in = 2.54 cm. So our conversion factor is : 1 in = 2.54 cm. Since we want to convert to cm, it goes on the top. ( Hint)
Converting by using Dimensional Analysis: inch to cm
Cancel units
10.0 in x1 in
2.54 cm
Now we cancel and collect units. The inches cancel out, leaving us with cm : the Target unit.
Converting by using Dimensional Analysis: inch to cm
10.0 in x
1 in
2.54 cm = 25.4 cm
Since the unit is correct, all is left to do the math ...
The Answer
Converting by using Dimensional Analysis: inch to cm
Lets check it out !!!!!! Find the 10 in mark and directly across at the cm side. What number do you find?
5) You go to Europe and decide to have a haircut. Your hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
Identify , line up, cancel out, multiply, check
8.0 cm 1 in
2.54 cm= ? in
Question: Is the conversion Factor the same? What’s the difference?
Converting by using Dimensional Analysis: inch to cm
• Convert 250 g into Kg
Identify , line up, cancel out, multiply, check
250 g x 1Kg = Kg
1000 g
Converting by using Dimensional Analysis: g to Kg
• Convert 1.5 Kg into g
• Identify : Given and Target unit
• Line up: Conversion Factor
1.5 kg x = g
Converting by using Dimensional Analysis: Kg to g
Q: Which conversion factor will you be using?1Kg = 1000g or 1000g= 1Kg
A more complex conversionkm to mhr s
kilometers into meters and hour into second. We can do both conversions at once using the same method as in the previous conversion.
Identify
80 kmhr
A more complex conversionkm to mhr s
Write down the _____and ____
Line up
80 km xhr
1 hr 3600 s
A more complex conversionkm to mhr s
First conversion factor is: 1 hour = 3600 sec.
Line up
80 km x
hr
1 hr x
3600 s
1000 m
1 km
A more complex conversionkm to mhr s
The second conversion factor is: 1 km = 1000 m.
Cancel out units
80 km x
hr
1 hr x
3600 s
1000 m
1 km=
A more complex conversionkm to mhr s
Check your units !!!If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.
ms
80 km x
hr
1 hr x
3600 s
1000 m
1 km=
80,000 m
3600 s=
ms
A more complex conversionkm to mhr s
The Answer!!
Problem1:Convert 1 year into seconds
yearseconds
A Very more complex conversionto finish at home today !!
1 y365 days
24h
1day
1 h
60s
1y= s
Problem2: Taft football needs 550 cm for a 1st down. How many yards is this?
550 cm
1 in
2.54 cm
= yd
cm yd
12in
1ft
1 yd
3 ft
Dimensional Analysis
Problem3: A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
1.3 m= pieces
cm pieces
Dimensional Analysis
Dimensional Analysis
•Problem5:How old are you in minutes?
Age in y= min
Units and Conversions HWDue: tomorrow
HomeworkHomework
How would you convert 2h 45 min to second
Convert 55.00 km/h to m/s
Scientific Notation
M x 10n
• M is the coefficient 1<M<10
• 10 is the base
• n is the exponent or power of 10
Other Examples:
5.45E+6
5.45 x 10^6
Numbers less than 1 will have a negative exponent.
Numbers bigger than 1 will have a positive exponent.
A millionth of a second is:
0.000001 sec
1.0E-6 1.0x10^-6
Limits of Measurement
• Accuracy and Precision
• Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.
Example: Accuracy• Who is more accurate (Susan or
Amy) when measuring a book that has a true length of 17.0cm?
Susan:
18.1cm, 16.0cm, 18.0cm, 17.1cm
Amy:
16.5cm, 16.0cm, 16.2cm, 16.3cm
• Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is regardless is it is close to the real value.
Example: Precision
Who is more precise when measuring the same 17.0cm book?
Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the following are precise, accurate or
both.
Accurate
Not Precise
Not Accurate
Precise
Accurate
Precise
Graduated Cylinder - Meniscus