IDENTIFY METRIC UNITS FOR MASS,
DISTANCE, TIME, TEMPERATURE,
VELOCITY, ACCELERATION, DENSITY,
FORCE, ENERGY & POWER
COS 12.0
WHAT YOU’LL LEARN
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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
UNITS 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.
DEFINITIONS
DERIVED UNIT
• measurement unit using a combination of
units
• g/cm3, m/s2, m/s, g/ml, kW
DISTANCE (LENGTH)
• measure of straight-line distance between
two points
• meter, kilometer, mile
MASS
• measure of amount of matter in an object
TIME
• measured period during which an action,
process, or condition exists or continues
• seconds, minutes, hours, days, years…
TEMPERATURE
• measure of average kinetic energy of all
particles in an object
• Kelvin
• absolute zero (0 K)
• coldest possible temperature
• = -273°C
VELOCITY
• measures the speed & direction of a moving
object
ACCELERATION
• rate of change of velocity, occurs if an
object speeds up, changes direction or slows
down
FORCE
• push or pull that one body exerts on another
ENERGY
• capacity to do work
POWER
• amount of work done or energy transferred
ELECTRIC CURRENT
• flow of electric charge through a wire or
conductor
DENSITY
• mass per unit volume of a material
VOLUME
• amount of space occupied by an object
• unit is liter
• 1 ml = 1 cm3
WEIGHT
• measure of gravitational force exerted on an
object
JOULE
• SI unit of energy measuring heat, electricity
and mechanical work
WATT
• SI deried unit of power, equal to one joule
of energy per second.
• measures a rate of energy use or production.
NEWTON
• SI derived unit of force
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
SIGNIFICANT FIGURES
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 measurement
Accuracy
• description of how close a measurement is to the
true value of the quantity measured
Chapter 1
Accuracy and Precision
Chapter 1
Accuracy and Precision
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.
Multiplying and Dividing
• RULE: When multiplying or dividing, your answer may only
show as many significant digits as the multiplied or divided
measurement showing the least number of significant digits.
• Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm
= 5946.50525 cm3
• We look to the original problem and check the number of
significant digits in each of the original measurements:
• 22.37 shows 4 significant digits.
• 3.10 shows 3 significant digits.
• 85.75 shows 4 significant digits.
• Our answer can only show 3 significant digits because that is
the least number of significant digits in the original problem.
• 5946.50525 shows 9 significant digits, we must round to the
tens place in order to show only 3 significant digits. Our final
answer becomes 5950 cm3.
Adding and Subtracting
• RULE: When adding or subtracting your answer can only
show as many decimal places as the measurement having
the fewest number of decimal places.
• Example: 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
decimal places shown in each of the original
measurements. 2.1 shows the least number of decimal
places.
• We must round our answer, 20.69, to one decimal place
(the tenth place).
• Our final answer is 20.7 g
SCIENTIFIC NOTATION
Scientific Notation
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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.
Scientific Notation
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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
Scientific Notation
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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
Standard Form
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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!
Write the following in scientific
notation:
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4,100,000 = _______________
4.1 x 106
345,600,000,000 = _________
3.456 x 1011
0.0456= ________________
4.56 x 10-2
0.00000012=____________
1.2 x 10-7
0.00305= ____________
3.05 x 10-3
Write the following in standard form:
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4.67 x 103 =__________________
4670
3.112 x 105 = _________________
311200
3.112 x 10-4 = ________________
0.0003112
4 x 10-6 = ___________________
0.000004
1 x 1011 = __________________
100,000,000,000
STANDARDS OF MEASUREMENT
WHY SI UNITS?
metric
• standard of measurement (for most nations)
• each type of SI measurement has a base unit
base unit
• fundamental unit of measurement which are
used to form other, compound units for other
quantities. (SI base unit)
What does SI stand for?

international system of units
SI PREFIXES

Easy to use because it is based on
multiples of ten.
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
KHDODCM
• 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
KHDODCM
• 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)
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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.
SI Prefix Conversions
0.2
20 cm = _______m
32
0.032 A = _______
mA
45,000 nm
45 m = _______
0.0805 km
805 dm = _________