1. Warm Up a) Order each set of numbers from least to greatest
104 , 10-2, 100, 10-1
10-2
10-1
100
104
82 , 8-2, 83, 80
8-2 80 82 83
23 , 2-6, 2-4, 21
2-6
2-4 21 23
Order the powers from least to greatest (10-4)5, (10-3)7, (10-8)-2. b)
10-20
10-21
1016 2 1 3

2. Lesson 3-3 Scientific Notation You'll Learn how to
Express large and small numbers in scientific Notation
Compare two numbers written in scientific Notation

3. Express large and small numbers in scientific Notation
An abbreviation or shorthand way of writing very large or very small numbers.
Distance from earth to the closest start outside our solar system
25,300,000,000,000 Kilometers
Number of atoms in a glass of water
30,600,000,000,000,000,000,000,000 atoms
Weight of a proton
grams

4. Write each number in scientific notation
Convert from standard form to scientific notation.
EXAMPLE 1
Write each number in scientific notation . .
Move the decimal point and count the number of spots, until there is exactly one digit to the left of the decimal point. 1) ₓ =
2.53
1013
Place the Decimal point in the new position and get rid of all the zeros
Count the number of spots . . 2) ₓ =
3.68
10-19
The sign of the exponent
Left (+)
Right (–)

5. Write each number in scientific notation
Your Turn ₓ 1) = 6
1017 ₓ 2) =
1.2
10-11 ₓ 3) =
7.09
10-3

6. Therefore 1st cell has a greater diameter
Science application
A certain cell has a diameter of approximately 4.11 ˣ 10-5 meters. A second cell has a diameter of 1.5 ˣ which cell has a greater diameter
EXAMPLE 3
4.11 ₓ 10-5
1st cell
Compare the powers of 10
1.5 ₓ 10-5
2nd cell
Compare the numbers
Therefore 1st cell has a greater diameter

7. Write each number in Standard notation
Convert from scientific notation to standard form
EXAMPLE 2
Write each number in Standard notation 1)
1.35 ₓ 108
Move the decimal point 8 places to the right then add in zeros in the empty spots =
1 35 . =
135 2)
2.7 ₓ 10-4
Move the decimal point 4 places to the left then add in zeros in the empty spots = .
2 7 . = . 2 7

8. Write each number in standard notation
Your Turn 1)
2.01 ₓ 107 = 2)
3.04 ₓ 10-3 =

9. Lesson Quiz: Part I
Write each number in standard notation.
 104
17,200
 10–3
0.0069
Write each number in scientific notation.
5.3  10–3
5.7  107
4. 57,000,000
5. Order the numbers from least to greatest. T 2  10–4, 9  10–5, 7  10–5
7  10–5, 9  10–5, 2  10–4

10. Lesson Quiz: Part II
6. A human body contains about 5.6  microliters of blood. Write this number in standard notation.
5,600,000

11. Lesson Quiz for Student Response Systems
1. Write the number in standard notation.
3.2  103
A. 32
B. 320
C. 3200 D 11

12. Lesson Quiz for Student Response Systems
2. Write the number in scientific notation.
0.0978
A  10–1
B  10–1
C  10–2
D  10–3 12

13. Lesson Quiz for Student Response Systems
3. Write the number in scientific notation.
13,432
A  104
B  10–4
C  10–4
D  104 13