cos 12.0 identify metric units for mass, distance, time, temperature, velocity, acceleration,...
TRANSCRIPT
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COS 12.0
IDENTIFY METRIC UNITS FOR MASS, DISTANCE, TIME, TEMPERATURE,
VELOCITY, ACCELERATION, DENSITY, FORCE, ENERGY & POWER
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WHAT YOU’LL LEARN• Name the prefixes used in SI & indicate what multiple of
ten each one represents.• Identify SI units and symbols for mass, length (distance),
time, temperature, velocity, acceleration, density, force, energy & power.
• Convert related SI units.• Use scientific notation & significant figures in problem
solving.• Identify the significant figures in calculations.• Understand the difference between precision & accuracy
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UNITS OF MEASUREMENTUNITS OF MEASUREMENT
What is a measurement?• A measurement is a number and a unit.• 14.5 meters, 35 dozen, and 1 hour are all
measurements.
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DEFINITIONS
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DERIVED UNIT
• measurement unit using a combination of units
• g/cm3, m/s2, m/s, g/ml, kW
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DISTANCE (LENGTH)
• measure of straight-line distance between two points
• meter, kilometer, mile
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MASS
• measure of amount of matter in an object
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TIME
• measured period during which an action, process, or condition exists or continues
• seconds, minutes, hours, days, years…
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TEMPERATURE
• measure of average kinetic energy of all particles in an object
• Kelvin
• absolute zero (0 K)
• coldest possible temperature
• = -273°C
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VELOCITY
• measures the speed & direction of a moving object
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ACCELERATION
• rate of change of velocity, occurs if an object speeds up, changes direction or slows down
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FORCE
• push or pull that one body exerts on another
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ENERGY
• capacity to do work
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POWER
• amount of work done or energy transferred
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ELECTRIC CURRENT
• flow of electric charge through a wire or conductor
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DENSITY
• mass per unit volume of a material
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VOLUME
• amount of space occupied by an object
• unit is liter
• 1 ml = 1 cm3
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WEIGHT
• measure of gravitational force exerted on an object
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JOULE
• SI unit of energy measuring heat, electricity and mechanical work
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WATT
• SI deried unit of power, equal to one joule of energy per second.
• measures a rate of energy use or production.
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NEWTON
• SI derived unit of force
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TABLE OF UNITS
Quantity Measured Unit Symbol
Mass Kilogram kg
Distance (length) Meter m
Time Second s
Temperature Kelvin K
Velocity m/s
Acceleration m/s2
Density kg/m3
Force Newtons N
Energy Joule J
Power Watt W
Electric current Ampere A
Volume Liter l
Bold letters indicate derived units
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SIGNIFICANT FIGURES
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SIGNIFICANT FIGURES
Significant figure • prescribed decimal place that determines the
amount of rounding off to be done based on the precision of the measurement
Precision • exactness of a measurementAccuracy • description of how close a measurement is to the
true value of the quantity measured
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Accuracy and PrecisionChapter 1
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Accuracy and PrecisionChapter 1
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Rules For Significant Digits Digits from 1-9 are always significant. Zeros between two other significant
digits are always significant One or more additional zeros to the
right of both the decimal place and another significant digit are significant.
Zeros used solely for spacing the decimal point (placeholders) are not significant.
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EXAMPLES OF SIGNIFICANT DIGITS
EXAMPLES # OF SIG. DIG. COMMENT
453 kg 3 All non-zero digits are always significant.
5057 L 4 Zeros between 2 sig. dig. are significant.
5.00 3 Additional zeros to the right of decimal and a
sig. dig. are significant.
0.007 1 Placeholders are not sig.
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Multiplying and DividingMultiplying and Dividing • RULE: When multiplying or dividing, your answer may only RULE: When multiplying or dividing, your answer may only
show as many significant digits as the multiplied or divided show as many significant digits as the multiplied or divided measurement showing the measurement showing the leastleast number of significant digits. number of significant digits.
• Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm= 5946.50525 cm33
• We look to the original problem and check the number of We look to the original problem and check the number of significant digits in each of the original measurements: significant digits in each of the original measurements:
• 22.37 shows 4 significant digits. 22.37 shows 4 significant digits. • 3.10 shows 3 significant digits.3.10 shows 3 significant digits.• 85.75 shows 4 significant digits.85.75 shows 4 significant digits.• Our answer can only show 3 significant digits because that is Our answer can only show 3 significant digits because that is
the least number of significant digits in the original problem.the least number of significant digits in the original problem.• 5946.50525 shows 9 significant digits, we must round to the 5946.50525 shows 9 significant digits, we must round to the
tens place in order to show only 3 significant digits. Our final tens place in order to show only 3 significant digits. Our final answer becomes 5950 cmanswer becomes 5950 cm33. .
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Adding and SubtractingAdding and Subtracting
• RULE: When adding or subtracting your answer can only RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having show as many decimal places as the measurement having the the fewestfewest number of decimal places. number of decimal places.
• Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 gExample: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g• We look to the original problem to see the number of We look to the original problem to see the number of
decimal places shown in each of the original decimal places shown in each of the original measurements. 2.1 shows the least number of decimal measurements. 2.1 shows the least number of decimal places. places.
• We must round our answer, 20.69, to one decimal place We must round our answer, 20.69, to one decimal place (the tenth place). (the tenth place).
• Our final answer is 20.7 g Our final answer is 20.7 g
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SCIENTIFIC NOTATION
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Scientific Notation• The number 123,000,000,000 in scientific notation is
written as : • 1.23 x 1011
• The first number 1.23 is called the coefficient. • It must be greater than or equal to 1 and less than 10. • The second number is called the base . • It must always be 10 in scientific notation. • The base number 10 is always written in exponent form. • In the number 1.23 x 1011 the number 11 is referred to as
the exponent or power of ten.
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Scientific Notation
• To write a number in scientific notation:• Put decimal after first digit and drop zeroes. • 1.23000000000• In number 123,000,000,000 coefficient will be 1.23 • To find exponent count number of places from
decimal to the end of number. • In 123,000,000,000 there are 11 places.• Therefore we write 123,000,000,000 as: • 1.23 x 1011
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Scientific Notation
• For small numbers we use a similar approach. • Numbers smaller than 1 will have a negative
exponent. • A millionth of a second (.000001) is:• 1.0 x 10-6
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Standard Form• Is just opposite of scientific notation!• 6.33 X 108 =• 633,000,000• All we’ve done is moved decimal eight (8) places to
right. • 5.18 X 10-7 =• .000000518• All we’ve done is moved decimal seven (7) places to left.• IT’S THAT EASY!
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Write the following in scientific notation:
• 4,100,000 = _______________• 345,600,000,000 = _________• 0.0456= ________________• 0.00000012=____________• 0.00305= ____________
4.1 x 106
3.456 x 1011
4.56 x 10-2
1.2 x 10-7
3.05 x 10-3
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Write the following in standard form:
• 4.67 x 103 =__________________• 3.112 x 105 = _________________• 3.112 x 10-4 = ________________• 4 x 10-6 = ___________________• 1 x 1011 = __________________
4670
311200
0.0003112
0.000004
100,000,000,000
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STANDARDS OF MEASUREMENT
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WHY SI UNITS?
metric• standard of measurement (for most
nations)• each type of SI measurement has a base
unitbase unit• fundamental unit of measurement which
are used to form other, compound units for other quantities. (SI base unit)
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What does SI stand for?
international system of units
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SI PREFIXES
Easy to use because it is based on multiples of ten.
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Prefix Symbol Multiplying factor
giga G 1000000000 or 109
mega M 1000000 or 106
kilo k 1000 or 103
hecto h 100 or 102
deka da (dk) 10 or 101
Base unit 0
deci dc .1 or 10-1
centi c .01 or 10-2
milli m .001 or 10-3
micro µ .000001 or 10-6
nano n .000000001 or 10-9
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K H D O D C M
• Changing from one metric unit to another is called metric conversion
• “M” is the space where meter, liter, or gram belongs or base unit (0)
• Let’s practice!• To change from one metric unit to another, we simply
move the decimal point.• For example:
25.4 km = ? cm• K-H-D-O-D-C is 5 places to the right• 25.4 km = 2,540,000 cm
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K H D O D C M
• 30 cm = ? hm• C – D- O –D- H is 4 places to the left• 30 cm = 0.0030 hm
(this is the same as 0.003 hm)• 14 dal = _____dl • D- O –D is 2 places to the right• 14 dal = 1400 dl• Find the difference between the exponents of the two
prefixes.• Move the decimal that many places.
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SI Prefix Conversions
20 cm = _______m
0.032 A = _______ mA
45 m = _______ nm
805 dm = _________ km
0.2
0.0805
45,000
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