Date
LESSON
73
Time
Scientific Notation
Complete the following pattern.
1.
102 10 10 100
2.
103 10 10 10 3.
104 4.
105 5.
106 Copyright © Wright Group/McGraw-Hill
Use the answers to Problems 1–5 to help you complete the following.
6.
2 102 2 100 200
7.
3 103 3 8.
4 104 9.
6 105 10.
8 106 When you write a number as the product of a number and a power of 10, you are using
scientific notation. Scientific notation is a useful way to write large or small numbers.
Many calculators display numbers one billion or larger with scientific notation.
Example:
In scientific notation, 4,000 is written as 4 103.
It is read as four times ten to the third power.
Write each of the following in standard notation and number-and-word notation.
Standard Notation
11.
5 103 12.
7 102 13.
2 104 14.
5 106 214
Number-and-Word Notation
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Created for Mr. Turner on 10/22/2010.
Date
LESSON
73
Time
History of Earth
Geologists, anthropologists, paleontologists, and other scholars often estimate when
important events occurred in the history of Earth. For example, when did dinosaurs
become extinct? When did the Rocky Mountains develop? The estimates are very
broad, partly because events like these lasted for many years and partly because
dating methods cannot precisely pinpoint exact times from so long ago.
Scientists base their estimates on the geological record—rocks, fossils, and other
clues—and on the bones and tools left long ago by humans. Below is a list of events
prepared by one group of scientists. Different estimates are given by other scientists.
Use the place-value chart on the next page to help you write, in standard notation, how
long ago the events below took place.
Copyright © Wright Group/McGraw-Hill
Example:
Earth was formed about 5 109 years ago. Find 109 on the place-value chart and
write 5 beneath it, followed by zeros in the cells to the right. Then use the chart to
help you read the number: 5 109 ⫽ 5 billion.
Event
Estimated Time
1.
Earth was formed.
5 109 years ago
2.
The first signs of life (bacteria cells) appeared.
4 109
3.
Fish appeared.
4 108
4.
Forests, swamps, insects, and reptiles appeared.
3 108
5.
The first dinosaurs appeared; the Appalachian
Mountains formed.
2.5 108
6.
Tyrannosaurus Rex lived; modern trees appeared.
1 108
7.
Dinosaurs became extinct.
6.5 107
8.
The first known human-like primates appeared.
6 106
9.
Woolly mammoths and other large ice-age mammals appeared.
8 105
Humans first moved from Asia to North America.
2 104
10.
Source: The Handy Science Answer Book
For use on electronic devices only.
Created for Mr. Turner on 10/22/2010.
215
Date
Time
LESSON
History of Earth
73
䉬
continued
Billion 100 M 10 M Million 100 Th 10 Th Thousand 100 10 One
109
108
107
106
105
104
103
102
101
100
1
2
3
4
5
6
7
8
9
10
Copyright © Wright Group/McGraw-Hill
Work with a partner to answer the questions. Write your answers in standard notation.
11.
According to the estimates by scientists, about how many years passed from the formation
of Earth until the first signs of life?
12.
About how many years passed between the appearance of the first fish and the appearance
of forests and swamps?
13.
According to the geological record, about how long did dinosaurs roam on Earth?
216
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Date
Time
LESSON
73
䉬
Expanded Notation
Each digit in a number has a value depending on its place in the numeral.
Example:
2,784
4
8
7
2
ones
or 4 ⴱ 1
or
tens
or 8 ⴱ 10
or
hundreds or 7 ⴱ 100
or
thousands or 2 ⴱ 1,000 or
4
80
700
2,000
Numbers written in expanded notation are written as addition expressions showing
the value of the digits.
Copyright © Wright Group/McGraw-Hill
1. a.
Write 2,784 in expanded notation as an addition expression.
b.
Write 2,784 in expanded notation as the sum of multiplication expressions.
c.
Write 2,784 in expanded notation as the sum of multiplication expressions using powers of 10.
2.
Write 987 in expanded notation as an addition expression.
3.
Write 8,945 in expanded notation as the sum of multiplication expressions.
4.
Write 4,768 in expanded notation as the sum of multiplication expressions using powers of 10.
5. a.
Write 6,125 in expanded notation as an addition expression.
b.
Write 6,125 in expanded notation as the sum of multiplication expressions.
c.
Write 6,125 in expanded notation as the sum of multiplication expressions using powers of 10.
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Created for Mr. Turner on 10/22/2010.
217
Date
Time
LESSON
Math Boxes
73
䉬
1.
3
Circle the fractions that are equivalent to ᎏ
.
8
6
ᎏ
12
9
ᎏ
24
8
ᎏ
3
2.
15
ᎏ
40
4
ᎏ
9
5
Charlene has 2ᎏᎏ yards of fabric. The
8
3
curtain she is making requires 3ᎏᎏ yards.
4
How much more fabric does she need?
66 67
3.
Find the missing numerator or denominator.
a.
4
ᎏ
10
c.
35
ᎏ
40
⫽
5
e. ᎏ
20
⫽
⫽
—
5
7
1
42
b. ᎏ
66
71
4.
Complete the “What’s My Rule?” table,
and state the rule.
⫽—
11
Rule
9
d. ᎏ
21
⫽
6
f. ᎏ
27
⫽
28
7
—
7
16
1
—
9
5
Copyright © Wright Group/McGraw-Hill
0
59
5.
Solve.
231 232
6.
a.
⫽ 32 / (16 / 2)
b.
⫽ (32 / 16) / 2
c.
(6.5 ⫹ 8.3) / (3 ⫺ 1) ⫽
d.
(4 ⴱ 12) ⫹ 8 ⫽
3
Lilia did 2ᎏᎏ hours of homework on
4
3
Saturday and ᎏᎏ hour of homework on
4
Sunday. What is the total time she spent
on homework over the weekend?
219
218
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70