1. 2-9 Scientific Notation Warm Up 1. 10 , 10 , 10 , 10 10 , 10 , 10 , 10
Course 3
2-9
Scientific Notation
Warm Up
Order each set of numbers from least to greatest.
, 10 , 10 , 10 4 –2 –1
10 , 10 , 10 , 10 4 –1 –2
2. 8 , 8 , 8 , 8 2 –2 3
8 , 8 , 8 , 8 3 2 –2
3. 2 , 2 , 2 , 2 3 –6 –4 1
2 , 2 , 2 , 2 3 1 –4 –6
, 5.2 , 5.2 , 5.2 2 9 –1 –2
5.2 , 5.2 , 5.2 , 5.2 9 2 –1 –2

2. 2-9 I CAN … express large and small numbers in scientific notation.
Course 3
2-9
Scientific Notation
I CAN … express large and small numbers in scientific notation.

3. Course 3
2-9
Scientific Notation
Vocabulary
scientific notation

4. Course 3
2-9
Scientific Notation
An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across.
The length of these numbers in standard notation makes them awkward to work with.
Scientific notation is a shorthand way of writing such numbers.

5. Course 3
2-9
Scientific Notation
In scientific notation the number of atoms in a penny is 2.0  1022, and the size of each atom is 3.0  10–8 centimeters across.
The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.
Helpful Hint

6. 2-9 Scientific Notation A. 1.35  105 1.35  10 10 = 100,000
Course 3
2-9
Scientific Notation
Additional Example 1A: Translating Scientific Notation to Standard Notation
Write the number in standard notation.
A  105
1.35  10 5
10 = 100,000 5
1.35  100,000
Think: Move the decimal right 5 places.
135,000

7. 2-9 Scientific Notation B. 2.7  10–3 1 2.7  10–3 10 = 1000 1 2.7 
Course 3
2-9
Scientific Notation
Additional Example 1B: Translating Scientific Notation to Standard Notation Continued
Write the number in standard notation.
B. 2.7  10–3
2.7  10–3
10 = –3 1
1000
2.7  1
1000
2.7  1000
Divide by the reciprocal.
0.0027
Think: Move the decimal left 3 places.

8. 2-9 Scientific Notation C. –2.01  104 –2.01  104 10 = 10,000
Course 3
2-9
Scientific Notation
Additional Example 1C: Translating Scientific Notation to Standard Notation Continued
Write the number in standard notation.
C. –2.01  104
–2.01  104
10 = 10,000 4
–2.01  10,000
–20,100
Think: Move the decimal right 4 places.

9. 2-9 Scientific Notation Write the number in standard notation.
Course 3
2-9
Scientific Notation
Try This: Example 1A
Write the number in standard notation.
A  109
2.87  10 9
10 = 1,000,000,000 9
2.87  1,000,000,000
2,870,000,000
Think: Move the decimal right 9 places.

10. 2-9 Scientific Notation Write the number in standard notation.
Course 3
2-9
Scientific Notation
Try This: Example 1B
Write the number in standard notation.
B. 1.9  10–5
1.9  10 –5 –5 1
10 =
100,000
1.9  1
100,000
1.9  100,000
Divide by the reciprocal.
Think: Move the decimal left 5 places.

11. 2-9 Scientific Notation Write the number in standard notation.
Course 3
2-9
Scientific Notation
Try This: Example 1C
Write the number in standard notation.
C. –5.09  108
–5.09  108
10 = 100,000,000 8
–5.09  100,000,000
–509,000,000
Think: Move the decimal right 8 places.

12. Course 3
2-9
Scientific Notation
Additional Example 2: Translating Standard Notation to Scientific Notation
Write in scientific notation.
Move the decimal to get a number between 1 and 10.
7.09
7.09  10
Set up scientific notation.
Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative.
Think: The decimal needs to move 3 places.
So written in scientific notation is 7.09  10–3.
Check  10–3 = 7.09  =

13. Course 3
2-9
Scientific Notation
Try This: Example 2
Write in scientific notation.
Move the decimal to get a number between 1 and 10.
8.11
8.11  10
Set up scientific notation.
Think: The decimal needs to move left to change 8.11 to , so the exponent will be negative.
Think: The decimal needs to move 4 places.
So written in scientific notation is 8.11  10–4.
Check  10 = 8.11  = –4

14. Additional Example 3: Application
Course 3
2-9
Scientific Notation
Additional Example 3: Application
A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to end, how many millimeters long would they be? Write the answer in scientific notation.
1 centimeter = 10 millimeters, so 18.7 centimeters = 187 millimeters
187 mm  10,000
Find the total length.
1,870,000 mm

15. Additional Example 3 Continued
Course 3
2-9
Scientific Notation
Additional Example 3 Continued
1.87  10
Set up scientific notation.
Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive.
Think: The decimal needs to move 6 places.
The 10,000 pencils would be 1.87  106 mm long, laid end to end. This is about one mile long.

16. 2-9 Scientific Notation Try This: Example 3
Course 3
2-9
Scientific Notation
Try This: Example 3
An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation.
Find the weight each cable is expected to hold by dividing the total weight by the number of cables.
2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable
Each cable can hold 300,000 pounds.
Now write 300,000 pounds in scientific notation.

17. Try This: Example 3 Continued
Course 3
2-9
Scientific Notation
Try This: Example 3 Continued
3.0  10
Set up scientific notation.
Think: The decimal needs to move right to change 3.0 to 300,000, so the exponent will be positive.
Think: The decimal needs to move 5 places.
Each cable can hold 3.0  10 pounds. 5

18. 2-9 Scientific Notation Lesson Quiz Write in standard notation.
Course 3
2-9
Scientific Notation
Lesson Quiz
Write in standard notation.
 104
17,200
 10–3
0.0069
Write in scientific notation.
5.3  10–3
5.7  107
4. 57,000,000
5. A human body contains about 5.6 x microliters of blood. Write this number in standard notation.
5,600,000