Order numbers in scientific notation

EXAMPLE 3

SOLUTION

STEP 1

Write each number in scientific notation, if necessary.

103,400,000 = 1.034 108 80,760,000 = 8.076 107

Order 103,400,000, 7.8 108, and 80,760,000 from least to greatest.

Order numbers in scientific notationEXAMPLE 3

STEP 2

Order the numbers. First order the numbers with different powers of 10. Then order the numbers with the same power of 10.

Because 107 < 108, you know that 8.076 107 is less than both 1.034 108 and 7.8 108. Because 1.034 < 7.8, you know that 1.034 108 is less than 7.8 108.

So, 8.076 107 < 1.034 108 < 7.8 108.

Order numbers in scientific notation

EXAMPLE 3

STEP 3

Write the original numbers in order from least togreatest.

80,760,000; 103,400,000; 7.8 108

Compute with numbers in scientific notation

EXAMPLE 4

Evaluate the expression. Write your answer in scientificnotation.

a. (8.5 102)(1.7 106)(8.5 • 1.7) (102 • 106)=

14.45 108=

(1.445 101)= 108

1.445 (101 )= 108

Commutative property andassociative propertyProduct of powers property

Write 14.45 in scientificnotation.

Associative property

1.445 109 = Product of powers property

Compute with numbers in scientific notation

EXAMPLE 4

b. (1.5 10 3)– 2 (10 3)– 2= 1.52

(10 6)–= 2.25

Power of a product property

Power of a power property

10−3

c. 1.2 104

1.6 =

10 3 –

1.21.6

10 4Product rule for fractions

(107)= 0.75

(7.5 10 1)– = 107

7.5 (10 1 – = 107)

(106)= 7.5

Quotient of powers property

Write 0.75 in scientific notation.

Associative property

Product of powers property

GUIDED PRACTICE for Examples 3 and 4

Order 2.7 105, 3.401 104, and 27,500 from least to greatest.

2.

ANSWER 27,500; 3.401 104, and 2.7 105

GUIDED PRACTICE for Examples 3 and 4

Evaluate the expression. Write your answer in scientific notation.

3. (1.3 10 5)– 2 (10 10)–= 1.69

10 2

4. 4.5 105

– 1.5 107= 3

5. (1.1 107) (4.2 102) 4.62 109=