Lesson 1.6 (8)

Course 3, Lesson 1-6
Write each expression using a positive exponent.
1. 7–6 2. (–10)–3 3. x–5
Simplify. Express using positive exponents.
4. 6–2 • 65 5.
6. –5x2y–2 • 3x–3y5n 7.
8. Order 11–3, 111, 113, 110, and 11–1 from least to greatest.


3
5
8
8


3 2
2
a b
a b

ANSWERS
1.
2.
3.
4. 63
5. 82
6.
7.
8. 11–3, 11–1, 110, 111, 113
6
1
7
 
3
1
10
5
1
x
 3
15y
x
b
a

WHY is it helpful to write numbers in
different ways?
The Number System

Course 3, Lesson 1-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 8.EE.4
Perform operations with numbers expressed in scientific notation,
including problems where both decimal and scientific notation are
used. Use scientific notation and choose units of appropriate size for
measurements of very large or very small quantities. Interpret
scientific notation that has been generated by technology.

Course 3, Lesson 1-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

To
• write numbers in standard form,
• write numbers in scientific notation
The Number System

• scientific notation
The Number System

The Number System
Words Scientific notation is when a number is written as the
product of a factor and an integer power of 10. When the
number is positive the factor must be greater than or equal
to 1 and less than 10.
Symbols , where 1 ≤ a < 10 and n is an integer
Example 425,000,000 =
×10na
84.25×10

1
Need Another Example?
Step-by-Step Example
1. Write the number in standard form.
5.34 × 104
5.34 × 104 = 53,400.

Answer
Write 9.62 × 105 in standard form.
962,000

1
2. Write the number in standard form.
3.27 × 10–3
3.27 × 10−3 = 0.00327

Answer
Write 2.85 × 10−5 in standard form.
0.0000285

1
2
3. Write the number in scientific notation.
3,725,000
3,725,000 = 3.725 × 1,000,000 The decimal point moves 6 places.
= 3.725 × 106 Since 3,725,000 > 1, the exponent is positive.

Answer
Write 931,500,000 in scientific notation.
9.315 × 108

1
2
4. Write the number in scientific notation.
0.000316
0.000316 = 3.16 × 0.0001 The decimal point moves 4 places.
= 3.16 × 10–4 Since 0 < 0.000316 < 1, the exponent is negative.

Answer
Write 0.0044 in scientific notation.
4.4 × 10−3

1
2
5. Refer to the table at the right.
Order the countries according
to the amount of money
visitors spent in the United
States from greatest to least.
1.06 × 107
Canada and
United Kingdom
↓
1.06 > 1.03
Group the numbers
by their power of 10.
Mexico
and India
↓
1.03 × 107
7.15 × 106
1.83 × 106
>
7.15 > 1.83
Compare the decimals.↑
United
Kingdom
↑
Canada
↑
Mexico
↑
India

Answer
The following table lists the maximum
frequency for the colors of the visible light
spectrum. List the colors from greatest to
least frequency.
violet, blue, green, orange, red

1
6. If you could walk at a rate of 2 meters per
second, it would take you 1.92 × 108 seconds to walk to
the moon. Is it more appropriate to report this time as
1.92 × 108 seconds or 6.09 years? Explain your reasoning.
The measure 6.09 years is more appropriate. The number
1.92 × 108 seconds is very large so choosing a larger unit
of measure is more meaningful.

Answer
One light year is about 9.46 × 1012 kilometers
or 9.46 × 1018 millimeters. Is it more appropriate
to report this length as 9.46 × 1012 kilometers or
9.46 × 1018 millimeters? Explain your reasoning.
9.46 × 1012 kilometers; the number is very large
so choosing a larger unit of measure is more
meaningful.

How did what you learned
today help you answer the
different ways?
The Number System

How did what you learned
today help you answer the
different ways?
The Number System
Sample answers:
• Scientists often use very large or very small numbers
which can be written in scientific notation.
• Scientific notation is a more concise way of writing
these numbers.

Explain the steps
used to write a number
between 0 and 1 in
scientific notation. Use
an example to illustrate
your explanation.
Ratios and Proportional RelationshipsThe Number System

Lesson 1.6 (8)

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Lesson 1.6 (8)