2. RULES
1. All nonzero digits are significant.
EXAMPLE:
1.694 g has 4 significant figures
1.6 g has 2 significant figures.
3. RULES
2. Zeroes in between nonzero digits are
considered significant.
EXAMPLE:
1005 kg has 4 significant figures
4.07 mL has 3 significant figures.
4. RULES
3. “Leading” zeroes, to the left of the first nonzero
digit, are never significant.
EXAMPLE:
0.001 C has only 1 significant figure
0.013 g has 2 significant figures.
5. RULES
4. Zeroes to the right of a decimal point in a
number are significant.
EXAMPLE:
0.029 mL has 2 significant figures
0.700 g has 3 significant figures
6. RULES
5. A number ends in zeroes that are not to the right
of a decimal point, the zeroes are not significant.
EXAMPLE:
5360.0 has five significant digits, but 5360 has only three
400.0 has four significant digits, but 400 has only one
8. RULE 1
If the digit to be dropped is greater than 5,
the last retained digit is increased by one.
EXAMPLE:
12.6 is rounded to 13
9. RULE 2
If the digit to be dropped is less than 5, the
last remaining digit is left as it is.
EXAMPLE:
12.4 is rounded to 12
10. RULE 3
If the digit to be dropped is 5, and if any digit
following it is not zero, the last remaining digit is
increased by one.
EXAMPLE:
12.51 is rounded to 13
11. RULE 4
If the digit to be dropped is 5 and is followed only
by zeroes, the last remaining digit is increased by one
if it is odd, but left as it is if even.
EXAMPLE:
11.5 is rounded to 12
12.5 is rounded to 12
13. SCIENTIFIC NOTATION
Standard Form
m x 𝟏𝟎𝒏
Coefficient
◾ equal or greater
than one, but
less than 10
base
exponent/power
◾ Can be positive
or negative
numbers
16. CONVERTING REGULAR NOTATION
TO SCIENTIFIC NOTATION
1.Move the decimal point to the right of the first (right-most) non-zero
number (NOTE: the exponent must be equal to the number of times you
movedthedecimal point).
2. When you move the decimal point to the left, the exponentis
positive.
3. When you move the decimal point to the right, the exponentis
negative.
18. CONVERTING SCIENTIFIC NOTATION TO
REGULAR NOTATION
1. If the value of the exponent is positive, remove the power of
ten and move the decimal point that value of places to the
right.
2. If the value of the exponent is negative, remove the power
of ten and move the decimal point that value of places to the
left.
20. WHAT IS MEASUREMENT
• It refers to the determination of the size or
magnitude of something.
• It is the comparison of an unknown quantity
with a standard quantity of the same rate
There are three important factors to consider when making
measurements:
•accuracy
•precision
•significant figures
21. PHYSICAL QUANTITY
A physical quantity is a characteristic or property of an object that
can be measured or calculated from other measurements
TWO TYPES
• Fundamental Quantities
Mass- It is a measure of the amount of matter in a body.
Length- It refers to the state,quality or fact of being long.
Time- It refers to the number of years, days, minutes, etc., representing
such an interval
• Derived Quantities
Examples:Velocity,Acceleration, Energy
22. SYSTEM OF UNITS
S.I / Metric System – refers to the International
System of Units. It provides a complete coherent
system of units used for physical quantities.
Length – meter (m)
Mass - gram (g)
Time – second (s
British System – Imperial System
Length- inch
Mass – pound
Time- second
23. • Metric System is accepted worldwide which was originally
described as MKS System (Meter-Kilogram- Second)
• It is also called the International system of units.
• The abbreviation SI comes from the systems French name
“Système International.”
• In this system, the units of length, mass, and time are the
meter, kilogram, and second, respectively.
• Other SI standards established by the committee are
those for temperature (the kelvin), electric current (the
ampere), luminous intensity (the candela), and the
amount of substance (the mole).
24.
25. UNITS
A quantity should be always compared with some
reference standard in order to measure.
Unit of a physical quantity is defined as the established
standard used for comparison of the given physical
quantity.
The units in which the fundamental quantities are
measured are called fundamental units and;
The units used to measure derived quantities are
called derived units.
26. Conversion of
Units
Some quantities need to be converted
because there are some cases that these
quantities are found complicated to use in
solving a word problem.
Conversion Factor
The ratio of a quantity stated in one unit
to the same quantity stated in another
unit.
27.
28. Conversion Factors
Length:
1m = 100cm = 1000mm
1km = 1000m = 0.6214mi
1m = 3.281 ft = 39.37 in
1cm = 0.3937in
1in = 2.54cm
1yd = 3ft = 91.44cm
1 ft = 12 in = 30.48 cm
1 mi = 5280 ft = 1.609 km
Time:
1 min = 60s
1 hr = 60 min = 3600s
1 day = 24hrs = 86 400s
1 yr = 365 days = 31, 536, 000s
1 yr = 52 weeks = 12 months
1 decade = 10 years
1 score = 20 years
1 century = 100 years
1 millennium = 10 centuries = 1000
years
29. Steps in Converting Units to Another
1. Multiply or divide by the appropriate conversion factor so that the
givenunitcancels,leavingthedesiredunitinthefinalresult.
Example:
How many feet does a car go in a 100-m dash?
Conversion factor:
1m = 3.28 ft
Solution:
1𝑚
100m x 3.28𝑓𝑡
= 328𝑓
𝑡
30. 2. If such conversion information cannot be found directly from a
table, you may use all known conversion factors so that all
necessarycancellationsofunitswilltake place.
Example:
How many centimeters are exactly in a mile?
Conversion factors:
1 mile = 1.61 km
1 km = 1000 m
1 m = 100 cm
Solutions:
1 mile x 1.61𝑘𝑚
1 𝑚𝑖𝑙𝑒
𝑥 1000𝑚
𝑥 100𝑐𝑚
= 161000𝑐𝑚
1𝑘𝑚 1𝑚
31. HOW TO CONVERT FROM ONE UNIT TO ANOTHER?
km hm dam m dm cm mm
0.00
5
0.05 0.5 5
7 70 700
0.2 2
0.06 0.6 6
35 350 3500 35000
Examples:
1.5km = 5000m
2.7m = 700cm
3.2mm =0.2cm
4.6cm =0.06m
5.35hm = 35000dm
35. COMBINATION UNIT CONVERSION
Help Stella determinethe speed in m/s if the
given speed is 33 km/h.
a. 16.9 m/s
b. 9.17 m/s
c.8.73 m/s
d. 19.24 m/s
36. COMBINATION UNIT CONVERSION
Leonard found that train he was travelling in
was running at 90 km/h while he was travelling.
This speed equals in m/s.
a. 19
b. 25
c. 28
d. 29
40. The weather forecaster says that the
probability that it will rain today is 75%.
Does it mean that there is a great chance
that it will rain today?
PROBABILITY
47. 1. What is the probability of picking red pen
out of the box?
Answer: 20%
It is unlikely to pick red pen out of the box
0
0%
IMPOSSIBLE
¼
0.25
25%
UNLIKELY
½
0.5
50%
As LIKELY
As UNLIKELY
1
100%
CERTAIN
¾
0.75
75%
LIKELY
48. 2. What is the probability of picking blue
pens out of the box?
Answer: 40%
It is unlikely to pick blue out of the box.
0
0%
IMPOSSIBLE
¼
0.25
25%
UNLIKELY
½
0.5
50%
As LIKELY
As UNLIKELY
1
100%
CERTAIN
¾
0.75
75%
LIKELY
49. 3. What is the probability of NOT picking
red pen out of the box?
Answer: 80%
It is likely to not pick red out of the box.
0
0%
IMPOSSIBLE
¼
0.25
25%
UNLIKELY
½
0.5
50%
As LIKELY
As UNLIKELY
1
100%
CERTAIN
¾
0.75
75%
LIKELY
54. PROBLEMS INVOLVING
PROBABILITIES
1. A student is chosen from a certain group.
There are 9 girls and 8 boys in that group.
What is the probability that the
chosen student is a boy?
Answer: 8/17 or 0.47 or 47%
55. 2. In John’s closet, there are 4 pairs of
blue socks, 5 pairs of green, and 2 pairs
of white socks, what is the probability that
John will get a pair of white socks?
Answer: 2/11 or 0.18 or 18%
56. WHAT ARE ODDS?
Odds is the ratio of the number of
favorable outcomes of the event to
the number of unfavorable
outcomes in reduced form.
57. HOW DO WE DISPLAY
THE ODDS FOR AN EVENT
𝒃
𝒂
or a :b
a – number of favorable outcomes
b – number of unfavorable outcomes
58. ODDS
EXAMPLE:
A box contains 4 green balls and 6 red balls. What
are the odds of randomly drawing a red ball?
SOLUTION:
6 FAVORABLE OUTCOMES
4 UNFAVORABLE OUTCOMES
So the Odds are 𝟔
= 𝟑
or 3 : 2
𝟒 𝟐
59.
60. ODDS
EXAMPLE 2:
What are the odds of randomly drawing a face
card from an ordinary full deck of playing
cards?
63. Example:
Suppose the odds that the Denver nuggets win the
basketball game this year are 2:11. What is the probability
that they win the basketball game this year?
SOLUTION:
Odds are 2:11
Therefore, P(E) =
𝒂
P(Win) =
𝒂+𝒃
𝟐
=
𝟐+𝟏𝟏
𝟐
𝟏
𝟑
64. EXAMPLE:
Consider a full-deck of playing cards shown below.
What is the probability of randomly drawing an ace?
What are the odds of randomly drawing an ace?
65. SOLUTION:
P (E) =
𝒂
Probability(Draw an ace) =
𝒂+𝒃
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐 𝒇 𝒂𝒄𝒆𝒔
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐 𝒇 𝒄𝒂𝒓𝒅𝒔
𝒂
𝒃
Odds for drawing an ace =
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐 𝒇 𝒂𝒄𝒆 𝒄𝒂𝒓𝒅𝒔
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐 𝒇 𝒏𝒐𝒕 𝒂𝒄𝒆 𝒄𝒂𝒓𝒅𝒔
69. PROBABILITY OF INDEPENDENT EVENTS
Example:
If you roll a six sided die and flip a
coin, what is the probability of rolling a five and
getting a head?
70. PROBABILITY OF INDEPENDENT EVENTS
Example:
A die and coin are tossed, what is
the probability of getting an even number and a
tail?
71. PROBABILITY OF DEPENDENT EVENTS
Dependent Events- are two events whose
result of the first event affects the outcome of
the other event
72. PROBABILITY OF DEPENDENT EVENTS
1. A box contains 3 red marbles, 4 green
marbles and 3 blue marbles. One marble is
removed from the box, and it is not replaced.
Another marble is drawn from the box. What is
the probability that the first marble is green, and
the second marble is blue.
73. PROBABILITY OF DEPENDENT EVENTS
2. A box of chocolates contains two milk
chocolates, five dark chocolates, and three
white chocolates. You randomly select and eat
three chocolates. Find the probability that you
select white chocolate, another white chocolate,
and then dark chocolate.
74. PROBABILITY OF DEPENDENT EVENTS
3. A box contains 7 red markers and 3 blue
markers. If we randomly select two markers
from this box, what is the probability drawing a
red marker and then a blue marker, without
replacement?
76. PROBABILITY
It is a measure that is associated
are of
with how certainwe
outcomes of a
particular
experiment or activity.
77. EXPERIMENT
It is a planned operation carried out
under controlled conditions.
The result of an experiment is called an
outcome.
78. SAMPLE SPACE
It is a set of all possible outcomes.
3 ways to represent a sample space,
◾list the possible outcomes
◾ create a tree diagram,
◾ create a Venn diagram
uppercase letter S
79. "OR" EVENT
The Or Rule states that we can find
the probability of either event A or event B
occurring by adding the probability of
event A and the probability of event B, as
long as both events are mutually exclusive:
P(A or B) = P(A) + P(B)
80. "OR" EVENT
Beth has a fruit basket which
contains 4 apples, 4 peaches, and 5
pears. If she randomly selects a piece of
fruit, what is the probability that it
or
is an apple a peach?
81. "OR" EVENT
A card is randomly selected from a
standard deck of 52 cards. What is
or
the probability that it is a 10 a face
card?
82. "AND" EVENT
If we want to find the probability of event A and
event B both occurring, we can use the And Rule.
The And Rule states that, if event A and event B
are independent, then:
P(A and B) = P(A) x P(B)
83. "AND" EVENT
Jason flips a coin and then rolls a six-
sided die. What is the probability that the
and
coin lands heads up the die shows an
84. "AND" EVENT
Alison, a teacher at a middle school has 5
boys and 6 girls in her class. Alison randomly
selects 3 different students to walk up and give
a presentation. Once the presentation is over the
student will leave for the day. What is the
probability that the first student is a boy, the
second student is a girl, and the third student is
also a girl?
85. COMPLEMENT
The complement of event A is denoted by A’ (read "A
prime"). It consists of all outcomes that are NOT in
A. Notice that P(A) + P(A’) = 1.
For example, let
S = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3, 4}
Then, A’ = {5, 6}.
86. COMPLEMENT
If you pull a random card from a deck of
playing cards, what is the probability it is not a
heart?
