Order numbers in scientific notation

1. 103,400,000 = 1.034 108 80,760,000 = 8.076 107 EXAMPLE 3 Order numbers in scientific notation Order 103,400,000, 7.8 108, and 80,760,000 from least to greatest. SOLUTION STEP 1 Write each number in scientific notation, if necessary.

2. Because 107 < 108, you know that 8.076107 is less than both 1.034108 and 7.8108. Because 1.034 < 7.8, you know that 1.034108isless than 7.8 108. So,8.076107<1.034108< 7.8108. EXAMPLE 3 Order numbers in scientific notation STEP 2 Order the numbers. First order the numbers with different powers of 10. Then order the numbers with the same power of 10.

3. 80,760,000; 103,400,000; 7.8 108 EXAMPLE 3 Order numbers in scientific notation STEP 3 Write the original numbers in order from least to greatest.

4. Commutative property and associative property a. (8.5 102)(1.7 106) = (8.5 • 1.7) (102 • 106) 108 14.45 = 108 (1.445 101) = 108 1.445 (101 ) = 1.445 109 = EXAMPLE 4 Compute with numbers in scientific notation Evaluate the expression. Write your answer in scientific notation. Product of powers property Write 14.45 in scientific notation. Associative property Product of powers property

5. – – 2 b. (10 3) (1.5 10 3) = 1.52 2 (107) (106) (10 6) = 0.75 = 2.25 – c. 1.2 104 10 4 = 1.2 – 10−3 10 3 1.6 1.6 – 107 (7.5 10 1) = – 107) 7.5 (10 1 = = 7.5 EXAMPLE 4 Compute with numbers in scientific notation Power of a product property Power of a power property Product rule for fractions Quotient of powers property Write 0.75 in scientific notation. Associative property Product of powers property

6. 2. Order 2.7  105, 3.401  104, and 27,500 from least to greatest. 27,500; 3.401  104, and 2.7  105 ANSWER for Examples 3 and 4 GUIDED PRACTICE

7. 107 5. (1.1 107) (4.2 102) – 3. (1.3 10 5) 2 (10 10) = 1.69 – 109 = 4.62 4. 4.5 105 = 3 10 2 1.5 – for Examples 3 and 4 GUIDED PRACTICE Evaluate the expression. Write your answer in scientific notation.