Download Zero and Negative Exponents

Lesson 7-2 Warm-Up
ALGEBRA 1
“Scientific Notation”
(7-2)
What is “scientific
notation”?
Scientific Notation: a way to write very large numbers in short form using powers of 10
in the form a x 10n, where n is an integer and a is between 1 and 10 (1 ≤ a ≤ 10).
Example: 7,500,000,000,000 (“7 trillion, 500 billion”) = 7.5 x 1012
How do you write a
number in scientific
notation?
To write a number in scientific notation, move the decimal so it’s after the first nonzero
(≠ 0) digit, write the rest of the nonzero numbers after the decimal, and multiply this by
10 to the power of the number of jumps it would take to make the original number (right
jumps = positive exponent and left jumps = negative exponent)
__._____ x 10 ___  decimal jumps it would take to make the number
 
first rest of
nonzero the nonzero
digit digits
What is “standard
notation”?
Standard Notation: the usual way to write a number using commas, etc.
Examples:
Standard Notation
Scientific Notation
3,600,000,000,000 =
= 3.6 x 1012 (3.6 trillion)
0.0000000000436 =
= 4.36 x 10-11
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
Is each number written in scientific notation? If not, explain.
a. 0.46  104
No; 0.46 is less than 1.
b. 3.25  10–2
Yes
c. 13.2  106
No; 13.2 is greater than 10.
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
Write each number in scientific notation.
a. 234,000,000
234,000,000 = 2.34  108
Move the decimal point 8 places to the
left and use 8 as an exponent.
Drop the zeros after the 4.
b. 0.000063
0.000063 =
6.3  10–5
Move the decimal point 5 places to the
right and use –5 as an exponent.
Drop the zeros before the 6.
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
Write each number in standard notation.
a. elephant’s mass: 8.8  104 kg
8.8  104 = 8.8000.
A positive exponent indicates a
number greater than 10. Move the
decimal point 4 places to the right.
= 88,000 kg
b. ant’s mass: 7.3  10–5 kg
7.3  10–5 = 0.00007.3
A negative exponent indicates a
number between 0 and 1. Move the
decimal point 5 places to the left.
= 0.000073 kg
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
List the planets in order of their distance from the
sun from least to greatest.
Planet
Distance from
the Sun
Jupiter
4.84  108 mi
Earth
9.3  107 mi
Neptune
2.8  109 mi
Mercury
3.8  107 mi
1. Order the powers of 10;
2. Arrange the decimals with the same power of 10 in order by place value.
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
(continued)
3.8  107
Mercury
9.3  107
Earth
4.84  108
Jupiter
2.8  109
Neptune
From least to greatest distance from the sun, the order of the planets
is Mercury, Earth, Jupiter, and Neptune.
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
Order 0.0063  105, 6.03  104, 6103, and 63.1  103 from
least to greatest.
Write each number in scientific notation.
0.0063  105
6.3  102
6.03  104
63.1  103
6103
6.03  104
6.103  103
6.31  104
Order the powers of 10. Arrange the decimals with the same power of 10
in order.
6.3  102
6.103  103
6.03  104
6.31  104
Write the original numbers in order.
0.0063  105
6103
6.03  104
63.1  103
ALGEBRA 1
Scientific Notation
LESSON 7-2
Additional Examples
Simplify. Write each answer using scientific notation.
a.
b.
6(8  10–4) = (6 • 8)  10–4
Use the Associative Property of
Multiplication.
= 48  10–4
Simplify inside the parentheses.
= 4.8  10–3
Write the product in scientific notation.
0.3(1.3  103) = (0.3 • 1.3)  103
Use the Associative Property of
Multiplication.
= 0.39  103
Simplify inside the parentheses.
= 3.9  102
Write the product in scientific notation.
ALGEBRA 1
Scientific Notation
LESSON 7-2
Lesson Quiz
1. Write each number in scientific notation.
a. 0.00627
6.27  10–3
b. 3,486,000
3.486  106
2. Write each number in standard form.
a. 9.4  104
94,000
b. 2.3  10–6
0.0000023
3. Order the following numbers from least to greatest.
0.98  10–1, 1.6  103, 2.4  10–1, 11  100
0.98  10–1, 2.4  10–1, 11  100, 1.6  103
4. Simplify. Write the answer in scientific notation.
7(6.1  10–2)
4.27  10–1
ALGEBRA 1