Transcript 1-3 - My CCSD

1-3
Measurements
1-3 Metric
Metric
Measurements
Warm Up
Problem of the Day
Lesson Presentation
Course 2
1-3 Metric Measurements
Warm Up
Find each value.
1. 10 2
3. 100
Course 2
100
2
10,000
2. 10 4
4. 100
10,000
3
1,000,000
1-3 Metric Measurements
Problem of the Day
3
4
Which is larger, 100 or 100 ? How do
you know?
1004 is larger; the power of 100 is
greater.
Course 2
1-3 Metric Measurements
Learn to identify, convert, and compare
metric units.
Course 2
1-3 Metric Measurements
Course 2
1-3 Metric Measurements
Additional Example 1: Choosing the Appropriate
Metric Unit
Choose the most appropriate metric unit for
each measurement. Justify your answer.
A. The amount of water a runner drinks each
day
Liters—The amount of water a runner drinks each
day is similar to the amount of water in a large
water bottle.
B. The length of a boat
Meters—The length of a boat is similar to the
length of several doorways.
C. The mass of a car
Kilograms—The mass of a car is similar to the
mass of several hundred textbooks.
Course 2
1-3 Metric Measurements
Check it Out: Example 1
Choose the most appropriate metric unit for
each measurement. Justify your answer.
A. The amount of liquid in 10 teardrops
Milliliters—The amount of liquid in 10 teardrops
is similar to the amount of liquid in several
eyedroppers.
B. The mass of a pencil eraser
Grams—The mass of a pencil eraser is
similar to the mass of a few paperclips.
C. The length of 15 soccer fields
Kilometers—The length of 15 soccer fields is
similar to the length of 10 football fields.
Course 2
1-3 Metric Measurements
The prefixes of metric units correlate to place values
in the base-10 number system. The table shows
how metric units are based on powers of 10.
You can convert units within the metric system by
multiplying or dividing powers of 10. To convert to a
smaller unit, you must multiply. To convert to a
larger unit, you must divide.
Course 2
1-3 Metric Measurements
Additional Example 2A: Converting Metric Units
Convert the measure.
530 cL to liters
530 cL = (530 ÷ 100) L
= 5.3 L
Course 2
100 cL = 1L, so divide
by 100.
Move the decimal point
2 places left: 530.
1-3 Metric Measurements
Additional Example 2B: Converting Metric Units
Convert the measure.
1,070 g to milligrams
1,070 g = (1070  1000) mg
= 1,070,000 mg
Course 2
1 g = 1000 mg, so
multiply by 1000.
Move the decimal
point 3 places right:
1,070,000.
1-3 Metric Measurements
Check It Out: Example 2A
Convert the measure.
980 dm to meters
980 dm = (980 ÷ 10) m
= 98 m
Course 2
10 dm = 1m, so divide
by 10.
Move the decimal point
1 places left: 980.
1-3 Metric Measurements
Check It Out: Example 2B
Convert the measure.
580 g to centigrams
580 g = (580  100) cg
= 58,000 cg
Course 2
1 g = 100 cg, so
multiply by 100.
Move the decimal
point 2 places right:
58,000.
1-3 Metric Measurements
Additional Example 3: Using Unit Conversions
t
to Make Comparisons
Elizabeth purchases one pumpkin that weighs
3 kg and another that weighs 2,150 g. Which
pumpkin weighs more? Use estimation to
explain why your answer makes sense.
You can convert the mass of Elizabeth’s pumpkin
to grams.
1 kg = 1000 g, so multiply
3 kg = (3  1,000) g
by 1,000.
Move the decimal point 3
= 3,000 g
places right: 3.000.
2,150 g is about 2 kg. Since 2 kg < 3 kg,
Elizabeth’s 3 kg pumpkin weighs more.
Course 2
1-3 Metric Measurements
Check It Out: Additional Example 3
Tyesha purchases a bag of potatoes that
weighs 2.5 kg and another bag that weighs
3,850 g. Which bag weighs more? Use
estimation to explain why your answer makes
sense.
You can convert the mass of Tyesha’s bag to
grams.
1 kg = 1000 g, so multiply
2.5 kg = (2.5 x 1,000) g
by 1,000.
Move the decimal point 3
= 2,500 g
places right: 2.500.
3,850 g is about 4 kg. Since 4 kg > 2.5 kg,
Tyesha’s 3,850 g bag weighs more.
Course 2
1-3 Metric Measurements
Lesson Quiz
Convert each measure.
1. 1,270 g to kilograms
1.27 kg
2. 890 cm to millimeters
8,900 mm
3. 750 mL to liter
0.75 L
4. 122 km to meters
122,000 m
5. 800 mg to grams
0.8 g
6. Rosa walks 1.5 km to the library. Meghan walks
2,200 m to the library. Who walks farther? Use
estimation to explain why your answer makes
sense. Meghan walks farther. 2,200 m = 2.2 km
Course 2
1-3
Measurements
1-4 Metric
Applying
Exponents
Warm Up
Problem of the Day
Lesson Presentation
Course
22
Course
1-3 Metric Measurements
Warm Up
Find each value.
1. 92
81
2. 122
144
3. 152
225
4. 102
100
5. 103
1,000
6. 104
10,000
Course 2
1-3 Metric Measurements
Problem of the Day
Each day, Lowell runs one more lap than
he did the day before. After seven days
he has run a total of 77 laps. How many
laps did he run on the first day? 8
Course 2
1-3 Metric Measurements
Learn to express large numbers in
scientific notation.
Course 2
1-3 Metric Measurements
Vocabulary
scientific notation
Course 2
1-3 Metric Measurements
The distance from Venus to the Sun is over
100,000,000 kilometers. You can write this
number as a power of ten by using a base of
ten and an exponent.
10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108
Power of ten
Course 2
1-3 Metric Measurements
The table shows several powers of ten.
Power of 10
Course 2
Meaning
Value
101
10
10
102
10 · 10
100
103
10 · 10 · 10
1,000
104
10 · 10 · 10 · 10
10,000
1-3 Metric Measurements
Additional Example 1A: Multiplying by
Powers of Ten
Multiply 14 · 103.
Method 1: Evaluate the power.
14 · 103 = 14 · (10 · 10 · 10)
= 14 · 1,000
= 14,000
Course 2
Multiply 10 by
itself 3 times.
Multiply.
1-3 Metric Measurements
Additional Example 1B: Multiplying by
Powers of Ten
Multiply 14 · 103.
Method 2: Use mental math.
14 · 103 = 14.000
3 places
= 14,000
Course 2
Move the decimal point 3
places.
(You will need to add 3
zeros.)
1-3 Metric Measurements
Check It Out: Example 1A
Multiply 12 · 102.
Method 1: Evaluate the power.
12 · 102 = 12 · (10 · 10)
= 12 · 100
= 1,200
Course 2
Multiply 10 by
itself 2 times.
Multiply.
1-3 Metric Measurements
Check It Out: Example 1B
Multiply 12 · 102.
Method 2: Use mental math.
12 · 102 = 12.00
2 places
= 1,200
Course 2
Move the decimal point 2
places.
(You will need to add 2
zeros.)
1-3 Metric Measurements
Scientific notation is a kind of shorthand that
can be used to write large numbers. Numbers
expressed in scientific notation are written as the
product of two factors. In scientific notation,
17,900,000 is written as
A number greater
than or equal to 1 but
less than 10
Course 2
A power of 10
1-3 Metric Measurements
Writing Math
In scientific notation, it is customary to use a
multiplication cross () instead of a dot.
Course 2
1-3 Metric Measurements
Additional Example 2: Writing Numbers in Scientific
Notation
Write the number 4,340,000 in scientific
notation.
6 places
Move the decimal point to
4,340,000 = 4,340,000 get a number that is greater
than or equal to 1 and less
than 10.
= 4.34  106 The exponent is equal to
the number of places the
decimal point is moved.
Course 2
1-3 Metric Measurements
Check It Out: Example 2
Write the number 8,421,000 in scientific
notation.
6 places
8,421,000 = 8,421,000
= 8.421  106
Course 2
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
The exponent is equal to
the number of places the
decimal point is moved.
1-3 Metric Measurements
Additional Example 3: Writing Numbers in Standard
Form
The population of China in the year 2000 was
estimated to be about 1.262  109. Write this
number in standard form.
Since the
9
1.262  10 = 1.262000000
exponent is 9,
move the decimal
point 9 places to
the right.
= 1,262,000,000
The population of China was about 1,262,000,000
people.
Course 2
1-3 Metric Measurements
Check It Out: Example 3
The distance from the Earth to the Sun is
calculated to be 1.5  108 kilometers. Write
this distance in standard form.
1.5  108 = 1.50000000
Since the exponent is
8, move the decimal
point 8 places to the
right.
= 150,000,000
The distance from the Earth to the Sun is about
150,000,000 kilometers.
Course 2
1-3 Metric Measurements
Additional Example 4: Comparing Numbers
in Scientific Notation
In 2005, the population of Mexico was 1.06  108
and the population of Brazil was 1.86  108. In
which country do more people live?
To compare numbers written in scientific notation,
first compare the exponents. If the exponents are
equal, then compare the decimal portion of the
numbers.
Mexico: 1.06  108
Brazil: 1.86  108
Notice that 1.06 < 1.86. So 1.06  108 < 1.86  108
Brazil has more people living there.
Course 2
1-3 Metric Measurements
Check It Out: Additional Example 4
The number of coins in Ty’s jar was 0.76  104
and number of coins in Laurel’s jar was
0.93  103. In which jar are there more coins?
To compare numbers written in scientific notation,
first compare the exponents. If the exponents are
equal, then compare the decimal portion of the
numbers.
Ty’s jar: 0.76  104
Laurel’s jar: .93  103
Notice that 4 > 3. So .76  104 > .93  103
Ty’s jar has more coins in it.
Course 2
1-3 Metric Measurements
Lesson Quiz: Part I
Multiply.
1. 25  102
2,500
2. 18  104
180,000
3. 110  102
11,000
4. 3.742  103
3,742
Course 2
1-3 Metric Measurements
Lesson Quiz: Part II
Write each number in scientific notation.
5. 7,400,000 7.4  106
6. 45,000
4.5  104
7. Earth is about 9.292  107 miles from the Sun.
Write this number in standard form.
92,920,000
Course 2