2. Example 1: Multiplication and Division with Scientific Notation
Main Idea
Example 1: Multiplication and Division with Scientific Notation
Example 2: Multiplication and Division with Scientific Notation
Example 3: Real-World Example
Example 4: Addition and Subtraction with Scientific Notation
Example 5: Addition and Subtraction with Scientific Notation
Lesson Menu

3. Compute with numbers written in scientific notation.
Main Idea/Vocabulary

4. Multiplication and Division with Scientific Notation
Evaluate (1.1 × 10–3)(2.5 × 109). Express the result in scientific notation.
(1.1 × 10–3)(2.5 × 109) = (1.1 × 2.5 )(10–3 × 109) Commutative and Associative Properties
= (2.75)(10–3 × 109) Multiply 1.1 by 2.5.
= 2.75 × 10– Product of Powers
= 2.75 × Add the exponents.
Answer: 2.75 × 106
Example 1

5. Evaluate (3.2 × 104)(1.9 × 10–8). Express the result in scientific notation.
B. 5.1 × 10–4
C × 10–4
D × 10–32
Example 1 CYP

6. Multiplication and Division with Scientific Notation
Evaluate Express the result in scientific notation.
Associative Property
Divide 7.75 by 2.5.
= 3.1 × 106 – (–2) Quotient of Powers
= 3.1 × 108 Subtract the exponents.
Answer: 3.1 × 108
Example 2

7. Evaluate . Express the result in scientific notation.
B. 3.5 × 10–4
C. 3.5 × 104
D. 3.5 × 1010
Example 2 CYP

8. PLANETS The largest planet in our solar system is Jupiter with a diameter of about 1.43 × 105 kilometers. The smallest planet in our solar system is Mercury with a diameter of about 4.9 × 103 kilometers. About how many times greater is the diameter of Jupiter than the diameter of Mercury?
Example 3

9. ≈ 2.9 × 101 Write 0.29 × 102 in scientific notation.
Associative Property
≈ 0.29 × 102 Simplify.
≈ 2.9 × 101 Write 0.29 × 102 in scientific notation.
Answer: The diameter of Jupiter is about 2.9 × or 29 times greater than the diameter of Mercury.
Example 3

10. ASTRONOMY The mass of Jupiter is about 1. 90 × 1027 kilometers
ASTRONOMY The mass of Jupiter is about × 1027 kilometers. The mass of Pluto is about 1.29 × 1022 kilometers. About how many times greater is the mass of Jupiter than the mass of Pluto?
A × 101 times greater
B × 105 times greater
C. 6.1 × 104 times greater
D. 6.1 × 105 times greater
Example 3 CYP

11. Addition and Subtraction with Scientific Notation
Evaluate (2.85 × 107) + (1.61 × 109). Express the result in scientific notation.
(2.85 × 107) + (1.61 × 109) = (2.85 × 107) + (161 × 107) Write 1.61 × 109 as × 107.
= ( ) × 107 Distributive Property
= × 107 Add and 1.61.
= × 109 Write × 107 in scientific notation.
Answer: × 109
Example 4

12. Evaluate (3.78 × 105) + (5.12 × 106). Express the result in scientific notation.
B × 105
C × 105
D × 106
Example 4 CYP

13. Addition and Subtraction with Scientific Notation
Evaluate (8.23 × 106) – (6.91 × 105). Express the result in scientific notation.
(8.23 × 106) – (6.91 × 105) = (82.3 × 105) – (6.91 × 105) Write 8.23 × 106 as × 105.
= (82.3 – 6.91) × 105 Distributive Property
= × 105 Subtract 6.91 from 82.3.
= × 106 Write × 105 in scientific notation.
Answer: × 106
Example 5

14. Evaluate (7.54 × 105) – (1.22 × 103). Express the result in scientific notation.
B × 104
C × 105
D × 104
Example 5 CYP