Download • Reading and Writing Decimal Numbers

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Math Course 2, Lesson 31
• Reading and Writing Decimal Numbers
• To read the decimal number 123.123:
Say “and” for the decimal point.
123 . 123:
“One hundred twenty-three and one
hundred twenty-three thousandths”
Say “thousandths” to conclude naming the number.
3
Examples: 0.3 = ___
Both are read “three tenths.”
10
21
0.21 = ____
Both are read “twenty-one hundredths.”
100
Practice:
Write each number as a decimal number.
1. Forty-nine and thirteen hundredths
2. Seven hundred eight and sixty-four thousandths
Use words to write each decimal number.
3. 38.459
4. 500.05
5. In the number 74.5604, which digit is in the thousandths place?
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Saxon Math Course 2
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Math Course 2, Lesson 32
• Metric System
Units of Length
Examples of Metric Prefixes
Unit
10 millimeters (mm) = 1 centimeter (cm)
kilometer (km)
1000 meters
hectometer (hm)
100 meters
dekameter (dkm)
10 meters
1000 millimeters (mm) = 1 meter (m)
100 centimeters (cm) = 1 meter (m)
1000 meters (m) = 1 kilometer (km)
Relationship
meter (m)
Units of Liquid Measure
decimeter (dm)
1
__
meter
1000 milliliters (mL) = 1 liter (L)
centimeter (cm)
1
___
meter
millimeter (mm)
1
____
meter
10
100
1000
Units of Mass
Celsius/Fahrenheit Scales
1000 grams (g) = 1 kilogram (kg)
1000 milligrams (mg)
An increase of 100°C on the
Celsius scale is equivalent to
an increase of 180°F on the
Fahrenheit scale.
= 1 gram
Practice:
Write the length of each segment in centimeters and in millimeters.
"
!
$
#
___
___
___
1. AB
2. AD
3. BD
4. The bag of grapes has a mass of 500 grams.
a. How many kilograms is that?
b. How many milligrams is that?
Saxon Math Course 2
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Math Course 2, Lesson 33
• Comparing Decimals
• Rounding Decimals
• To round a number:
1. Circle the place value you are rounding to.
2. Underline the digit to its right.
3. Ask “Is the underlined number 5 or more?”
Yes
Add 1 to the circled number.
No
Circled number stays the same.
4. Replace the underlined number (and any numbers after it) with zero.
67
○
329
○
Examples:
70
300
• Terminal zeros are zeros at the end of a number to the right of the decimal point.
They have no value.
Example: 1.3 = 1.30 = 1.300 = 1.3000
• To compare decimal numbers, it helps to insert or delete terminal zeros
so that both numbers have the same number of digits after the decimal point.
Then compare digits in each place from left to right.
Examples: 0.12 ○ 0.012
0.4 ○ 0.400
0.120 ○
> 0.012
0.4 ○
= 0.4
• After rounding decimal numbers, remove all terminal zeros after the decimal point.
Example: Round 3.14159 to the nearest hundredth.
3.1 ○
4 159
3.14000
3.14
Practice:
Compare 1–3.
1. 4.73 ○ 4.09
2. 0.27
○
1.0
3. 5.618
○
5.861
4. Estimate the sum of 7.08, 4.901, and 3.521 by rounding each number to the
nearest whole number before adding.
5. Round 1154.07085 to the nearest thousandth.
6. Round 1154.07085 to the nearest thousand.
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Saxon Math Course 2
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Math Course 2, Lesson 34
• Decimal Numbers on the Number Line
• The metric system uses decimals, not fractions.
Example: Find the length of this segment:
cm
1
2
3
a. in millimeters. 23 mm
b. in centimeters. 2.3 cm
Example: Find the number on the number line indicated by each arrow.
A
4.05
4.0
B
4.38
4.1
4.2
4.3
C
4.73
4.4
4.5
4.6
4.7
4.8
4.9
5.0
Sometimes adding a zero to the end of each number on the decimal
number line helps you to locate decimal numbers.
Example: 4.38 is between 4.30 and 4.40.
The number halfway between two numbers is the average (mean) of
the two numbers.
Practice:
1. How many millimeters equal 40.7 cm?
2. What decimal number is halfway between 20 and 21?
3. What decimal number is halfway between 2.7 and 2.8?
4. What decimal number names each point on this number line?
A
70
a. A
Saxon Math Course 2
B
C
70.1
b. B
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c. C
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Math Course 2, Lesson 35
• Adding, Subtracting, Multiplying,
and Dividing Decimal Numbers
Decimals Chart
+/−
×
÷ by whole
÷ by decimal
A. Line up the
B. Multiply. Then count C. Decimal
D. Decimal point
decimal points.
decimal places.
point is up.
is over, over, up.
E. 1. Place a decimal point to the right of a whole number.
F. 2. Fill empty places to the right of the decimal point with zeros.
Examples:
A, E, and F
3.6
0.36
+ 36.
39.96
5.00
–
4.32
_______
0.68
0.23
× 0.4
______
0.092
A and E
B
C and F
2 places
0.0018
_______
8)0.0144
1 places
3 places
Practice:
Simplify 1–4.
1. (6.3)(2.4)(1.2)
2. 1.55 ÷ 5
3. 29.71 – 3.087
4. 2.2 + 0.54 + 12
5. If the product of seven tenths and two tenths is subtracted from
the sum of eight tenths and five tenths, what is the difference?
6. What is the area and perimeter of a rectangle that is 1.3 meters wide and
0.9 meter long?
a. area:
b. perimeter:
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Saxon Math Course 2
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Math Course 2, Lesson 36
• Ratio
• Sample Space
• Ratio is a way to describe a relationship between two numbers.
Example: In a class of 28 students, there are 12 boys. What is the boy-girl
ratio? What is the girl-boy ratio?
1. Find the number of girls
in the class.
12 boys
12 boys
+ ? girls
28 total
+ 16 girls
28 total
2. Write the ratios as reduced
fractions.
boys
3
12 = __
_____
= ___
16
4
girls
girls
16
4
_____
___
__
boys = 12 = 3
number of favorable outcomes
• Probability = ____________________________
number of possible outcomes
• A sample space is the list of all possible outcomes for an event.
Example: One coin toss has two possible outcomes.
Sample space = {heads, tails}
Coin 1
• A tree diagram shows all the possible
outcomes of two events that occur at
the same time, such as tossing two coins.
Coin 2
Outcome
H
H H
T
H T
H
T H
T
T T
H
T
• The Fundamental Counting Principal says:
If there are m ways for A to occur, and n ways for B to occur, then there are m × n
ways for A and B to occur together.
Example: There are 2 × 6, or 12 outcomes for tossing a coin and a
number cube.
Practice:
1. In a box of pens, the ratio of red pens to blue
pens is 3 to 2. What fraction of the pens are blue?
2. What is the probability of tossing heads with one coin toss?
3. A coin is tossed and a number cube is rolled.
One possible outcome is H3 (heads, 3).
What is the sample space for the experiment?
Saxon Math Course 2
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Math Course 2, Lesson 37
• Area of a Triangle
• Rectangular Area, Part 2
A triangle has
three sides, and
any side can
be the base. A
triangle may have
three base-height
orientations, as
shown by rotating
these triangles.
One Right Triangle Rotated to Three Positions
height
height
height
base
base
base
One Obtuse Triangle Rotated to Three Positions
height
height
height
base
base
base
bh
1 bh or ___
Area of a triangle = __
2
2
• To find the area of a complex shape:
Example:
10 cm
1. Divide the shape into rectangular parts.
2. Find the area of each part.
3. Add the areas to find the total area.
Sometimes subtracting a “ghost” area
(the area that is missing)
from a larger rectangle that
includes the entire figure is easier.
10
7 cm
23 cm
There are three ways to find
the area of this shape.
10
C
50
(13)
A
120
12
12 cm
B
(65)
(5)
(5)
12
12
B
91
(13)
10
D
161
7
A
276
7
7
23
23
23
120 91 211 cm2
50 161 211 cm2
276 65 211 cm2
Practice:
Find the area of each figure.
1.
3 in.
6 in.
5 in.
2.
13 cm
5 cm
3.
8.6 ft
8.6 ft
7 ft
6 cm
6 cm
7 ft
10 ft
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Saxon Math Course 2
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Math Course 2, Lesson 38
• Interpreting Graphs
Bar graph
Number of Aluminum Cans
Collected by Each Homeroom
Number of Aluminum Cans
Pictograph
Doughnut Sales
Jan.
Feb.
Mar.
Represents 10,000 doughnuts
10,000
8,000
6,000
4,000
2,000
0
12
14
16
18
Score
Room Number
Line graph
Circle graph
Paul’s Game Scores
Where Dina
Spends Her Day
100
90
80
70
60
50
40
30
20
10
0
Elsewhere
4 hr
At home
12 hr
1
2
3
4
5
At school
8 hr
6
Game
Practice:
Use information from the graphs above to answer each question.
1. How many more doughnuts were sold in March than in January?
2. Which homeroom collected twice as many cans as homeroom 18?
3. To the nearest whole number, what was Paul’s average score?
4. True or false? Dina spends 60% of her time at home.
Saxon Math Course 2
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Math Course 2, Lesson 39
• Proportions
• A proportion is a statement that two ratios are equal.
Example: 5 · 16 = 80
16 =
___
20
4
__
20 · 4 = 80
5
Solve a proportion by finding the missing term.
1. Find the cross products.
2. Divide the known product by the known factor.
Example:
3 = __
6
__
5
W
3 ∙ W = 5 ∙ 6
3W = 30
30
W = ___
3
W = 10
Practice:
Solve 1–6.
0.4
16 = ___
1. ___
r
4
a
7 = ___
2. ___
40
20
21
24 = ___
3. ___
t
32
b
1.5 = ___
4. ___
45
2.5
c
0.45 = ___
5. _____
2.7
8.1
28
w = ___
6. ___
70
50
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Saxon Math Course 2
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Math Course 2, Lesson 40
• Sum of the Angle Measures of a Triangle
• Angle Pairs
90°
• A square has four angles and each one measures 90°.
90°
90°
By drawing a diagonal segment from one corner to the
opposite corner, the square divides into two congruent
triangles.
90°
• A triangle has three angles and the sum of those angles
is 180°.
45°
Adjacent angles share a common side.
90°
45°
Examples: ∠1 and ∠4, ∠x and ∠y
50°
Supplementary angles are two angles whose sum is 180°.
y
x
Examples: ∠y and ∠z, ∠3 and ∠4
z
A
Complementary angles are two angles whose sum is 90°.
Example: ∠A and ∠B
C
B
2
3
1
Vertical angles are a pair of non-adjacent angles formed by
two intersecting lines and have the same measure.
Examples: ∠1 and ∠3, ∠2 and ∠4, ∠x and ∠z
4
Practice:
1. If one angle of a right triangle measures 60˚, then
what are the measures of the other two angles?
Find each angle measure in this figure.
d
c
o
b 60
55o
a
2. m∠ a =
3. m∠b =
4. m∠ c =
5. m∠d =
Saxon Math Course 2
© Harcourt Achieve Inc. and Stephen Hake. All rights reserved.
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