1. Unit I Units and Measurement
Objectives - Express lengths, mass, time in SI units. - SI metric system - Convert distances between different units. - Describe time intervals in hours, minutes, and seconds. - Convert time in mixed units to time in seconds. - Describe the mass of objects in grams and kilograms.

2. It All Starts with a Ruler!!!

3. I. Two Systems of Units
a. Metric system and International System of Units
meter
kilogram
second
Kelvin
b. English system
inches, feet, yards, and miles.
pound
Fahrenheit

4. II. SI units meter (m): unit of length kilogram (kg): unit of mass
second (s): unit of time

5.  meter, (SI unit symbol: m), is the fundamental unit of length in the International System of Units (SI).
Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level).
Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."
National Prototype Metre Bar ( alloy of ninety percentplatinum and ten percent iridium) in  International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France.

6.  kilogramme ( kg), is the base unit of mass in the International System of Units (SI)
Is defined as being equal to the mass of the International Prototype of the Kilogram (platinum–iridium alloy) in International Bureau of Weights and Measures in Sèvres, France

7. Second (sec or s)
The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

8. 1. SI UNITS (Systéme Internationale)

9. Examples
The units for length, mass, and time (as well as a few others), are regarded as base SI units.
These units are used in combination to define additional units for other important physical quantities such as force and energy.

10. Definition (incomplete)[n 1]
2. SI base units
Unit name
Unit symbol
Quantity name
Definition (incomplete)[n 1]
Dimension symbol
metre m
length
Original (1793): 1/  of the meridian through Paris between the North Pole and the Equator.FG
Interim (1960):   wavelengths in a vacuum of the radiationcorresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.
Current (1983): The distance travelled by light in vacuum in 1/ second. L
kilogram[n 2] kg
mass
Original (1793): The grave was defined as being the weight [mass] of one cubic decimetre of pure water at its freezing point.FG
Current (1889): The mass of the international prototype kilogram. M
second s
time
Original (Medieval): 1/86400 of a day.
Interim (1956): 1/  of the tropical year for 1900 January 0 at 12 hours ephemeris time.
Current (1967): The duration of   periods of the radiation corresponding to the transition between the two hyperfine levels of theground state of the caesium 133 atom. T

11. Definition (incomplete)[n 1]
Unit name
Unit symbol
Quantity name
Definition (incomplete)[n 1]
Dimension symbol
ampere A
electric current
Original (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius creates a field of one oersted at the centre.[39] IEC
Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length. I
kelvin K
thermodynamic temperature
Original (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water.
Interim (1954): The triple point of water (0.01 °C) defined to be exactly K.[n 3]
Current (1967): 1/273.16 of the thermodynamic temperature of the triple point of water Θ
mole
mol
amount of substance
Original (1900): The molecular weight of a substance in mass grams.ICAW
Current (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in kilogram of carbon 12.[n 4] N
candela cd
luminous intensity
Original (1946): The value of the new candle is such that the brightness of the full radiator at the temperature of solidification ofplatinum is 60 new candles per square centimetre.
Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012hertz and that has a radiant intensity in that direction of 1/683 watt persteradian. J

12. 3. The Metric System
The metric system is a measurement system based on our decimal (base 10) number system.
Other countries and all scientists and engineers use the metric system for measurement.

13. Metric Prefixes Prefix Symbol Factor Number Factor Word Kilo- k 1000
Metric Units
The metric system has prefix modifiers that are multiples of 10.
Prefix
Symbol
Factor Number
Factor Word
Kilo- k
1000
Thousand
Hecto- h
100
Hundred
Deca-
da or dk 10
Ten
Unit
m, l, or g 1
One
Deci- d .1
Tenth
Centi- c
.01
Hundredth
Milli- m
.001
thousandth

14. C) unit convert chart

15. To change the scale of the base units, prefixes are attached
To change the scale of the base units, prefixes are attached. A prefix represents a factor by which the base unit must be multiplied. Metric prefixes are listed below (The prefixes most-commonly used in chemistry are listed in red):
Prefix
Symbol
Decimal
Value
Power of Ten
Exa- E
1,000,000,000,000,000,000
1018
Peta- P
1,000,000,000,000,000
1015
Tera- T
1,000,000,000,000
1012
Giga- G
1,000,000,000
109
Mega- M
1,000,000
106
Kilo- k
1,000
103
Hecto- h
100
102
Deka- da 10
101
(no prefix) 1
Deci- d .1
10-1
Centi- c
.01
10-2
Milli- m
.001
10-3
Micro-
10-6
Nano- n
10-9
Pico- p
10-12
Femto- f
10-15
Atto- a
10-18

16. Place Values of Metric Prefixes
Thousand
Hundred
Ten
One
Tenth
Hundredth
Thousandth km kg kL hm hg hL
dkm
dkg
dkL m g L dm dg dL cm cg cL mm mg mL

17. Meters Meters measure length or distance
One millimeter is about the thickness of a dime.

18. Meters One centimeter is about the width of a large paper clip
or your fingernail.

19. Meters
A meter is about the width of a doorway

20. Meters A kilometer is about six city blocks or 10 football fields.
1.6 kilometers is about 1 mile

21. Gram
Grams are used to measure mass or the weight of an object.

22. Grams
A milligram weighs about as much as a grain of salt.

23. Grams 1 gram weighs about as much as a small paper clip.
1 kilogram weighs about as much as 6 apples or 2 pounds.

24. Liters
Liters measure liquids or capacity.
2 Liter Soda

25. Liter
1 milliliter is about the amount of one drop

26. Liter
1 liter is half of a 2 liter bottle of Coke or other soda

27. Liter
A kiloliter would be about liter bottles of pop

28. III. THE CONVERSION OF UNITS
1. By multiply or divide by a power of 10 – for unit change in metric system only
To change from one unit to another in the metric system you simply multiply or divide by a power of 10.

29. To change from a larger unit to a smaller unit, you need to multiply.
1 km x 1000 = 1000 m
1 m x 100 = 100 cm
1 cm x 10 = 10mm

30. Place Values of Metric Prefixes
Move the decimal point to the right to multiply.
Thousand
Hundred
Ten
One
Tenth
Hundredth
Thousandth km kL kg hm hL hg
dkm
dkL
dkg m L g dm dL dg cm cL cg mm mL mg

31. Place Values of Metric Prefixes
Thousand
Hundred
Ten
One
Tenth
Hundredth
Thousandth km kg kL hm hg hL
dkm
dkg
dkL m g L dm dg dL cm cg cL mm mg mL

32. To change from smaller units to larger units you divide by a power of ten.
1000mm ÷ 10 = 100cm
100cm ÷ 10 = 10dm
10dm ÷ 10 = 1m

33. Place Values of Metric Prefixes
Move the decimal point to the left to divide.
Thousand
Hundred
Ten
One
Tenth
Hundredth
Thousandth km kL kg hm hL hg
dkm
dkL
dkg m L g dm dL dg cm cL cg mm mL mg

34. Place Values of Metric Prefixeskm kg kL hm hg hL
dkm
dkg
dkL m g L dm dg dL cm cg cL mm mg mL
3km
30hm
300dkm
3000m 4L
30000dm
300000cm
12cm mm

35. 2. The “Factor-Label” Method
Units, or “labels” are canceled, or “factored” out

36. Factor Label Method:
Regardless of conversion, keeping track of units makes things come out right
Must use conversion factors
- The relationship between two units
Canceling out units is a way of checking that your calculation is set up right!

37. Steps: 1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.

38. example: write 254 cm in km unit
example: write 254 cm in km unit for 1 km=1000 m=1000m x 100𝑐𝑚 1𝑚 =100000cm
Lining up conversion factors:
1𝑘𝑚 𝑐𝑚 = 𝑐𝑚 1𝑘𝑚 =1
Multiply proper factor:
254 cm = 254cm× 1𝑘𝑚 𝑐𝑚 = km

39. Example 1: Convert 3m to cm
For meters to cancel out, meters in the conversion factor must be on the opposite side of the fraction (fence). 3m
100 cm 1m
Given
Conversion Factor
Multiply every number on top of the fence and divide by the bottom.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

40. Example 2: Convert 1516 g to kg
conversion factor
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

41. Whiteboard Problem 1 Convert 1200 cm to m.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

42. Whiteboard Problem 2 Convert 5200 mL to L.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

43. Example 3: Convert 7200mm to km
100,000 cm
10 mm
1 cm
= km
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

44. Whiteboard Problem 3 Convert 3 m to mm.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

45. 3. relation between different units
1 ft = m
1 mi = km
1 liter = 10-3 m3

46. example: for 1 in=2.54 cm 1 in = 2.54 cm = 1 2.54 cm 2.54 cm
Lining up conversion factors:
= 1
1 in = 2.54 cm
2.54 cm cm
1 =
1 in = 2.54 cm
1 in in

47. Common conversion factors
English Factor
1 gallon = 4 quarts 4 qt/gal or 1gal/4 qt
1 mile = 5280 feet ft/1mile or 1 mile/5280 ft
1 ton = 2000 pounds lb/1ton or 1 ton/2000 lb
Common English to Metric
1 liter = quarts qt/1L or 1 L/1.057 qt or L/1qt
1 kilogram = 2.2 pounds lb/1kg or 1 kg/2.2 lb
or kg/1lb
1 meter = yards yd/1m or 1m/1.094 yd
or 0.917m/1yd
1 inch = 2.54 cm cm/inch or 1 in/2.54 cm

48. Non-Metric (English) Unit Conversions
Common Conversion Factors
5280 ft = 1 mile
12 in = 1 ft
1 mile = 1600 m
1 in = 2.54 cm
3 ft = 1 yard
English to Metric conversion factors
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

49. Example 4: Convert 2 miles to ft
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

50. Whiteboard Problem 4 Convert 3.2 ft to inches.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

51. Example 5: Convert 5 ft to cm
12 in
1 ft
2.54 cm
1 in
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

52. Whiteboard Problem 5 Convert 50 inches to m.
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

53. Problems Convert 45 inches to cm. 45 𝑖𝑛 1 ∙ 2.54𝑐𝑚 1𝑖𝑛 = 114.3 cm
Convert 8 m to inches.
8𝑚 1 ∙ 100𝑐𝑚 1𝑚 1𝑖𝑛 2.54𝑐𝑚 = 315𝑖𝑛
CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

54. Example 1.1
Grandma traveled 27 minutes at 44 m/s.
How many miles did Grandma travel?
44𝑚 𝑠 = 44𝑚 1609𝑚 𝑚𝑖𝑙𝑒 1𝑠 60𝑠 𝑚𝑖𝑛 =44× mile/min=1.64mile/min
27𝑚𝑖𝑛× 1.64𝑚𝑖𝑙 𝑚𝑖𝑛 =44.3𝑚𝑖𝑙𝑒𝑠
44.3 miles

55. (3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1
convert
Example 1 The World’s Highest Waterfall
The highest waterfall in the world is Angel Falls in Venezuela,
with a total drop of m. Express this drop in feet.
Since feet = 1 meter, it follows that
(3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1
For meter  feet:

56. A football field is 100 yards long.
Convert 100km to miles
A football field is 100 yards long.
What is this distance expressed in meters?

58. Reasoning Strategy: Converting Between Units
3. Summary
Reasoning Strategy: Converting Between Units
1. In all calculations, write down the units explicitly.
2. Treat all units as algebraic quantities. When
identical units are divided, they are eliminated
algebraically.
3. Use the conversion factors in reference tables. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation.

59. IV. time Two ways to think about time: What time is it?
3 P.M. Eastern Time on April 21, 2004,
How much time has passed?
3 hr: 44 min: 25 sec.
A quantity of time is often called a time interval.

60. Converting Mixed Units
You are asked for time in seconds.
You are given a time interval in mixed units.
1 hour = 3,600 sec minute = 60 sec
Do the conversion:
1 hour = 3,600 sec
26 minutes = 26 × 60 = 1,560 sec
Add all the seconds:
t = 3, , = 5, sec

61. Time Units

62. E) Practice
Example 2 Interstate Speed Limit
Express the speed limit of 65 miles/hour in terms of meters/second.
Use 5280 feet = 1 mile and 3600 seconds = 1 hour and
3.281 feet = 1 meter.

63. More practice 1. Convert 789 cm2 to m2 2. Convert 75.00 km/h to m/s
1m=100cm, 1m2=100cm *100cm=10000cm2
789 𝑐𝑚 2 =789 𝑐𝑚 2 × 1 𝑚 𝑐𝑚 2 = 𝑚 2
2. Convert km/h to m/s
km x 1000 m x 1 h___ = 20.83m/s
h km s