Warm Up

1. Evaluate 52

– 3

ANSWER 8125

4–7 432. Evaluate

ANSWER 1256

3. Simplify 6a –4 b 0.

ANSWER 6 a4

4. Simplify 8x3y –4

12x2y –3 .

ANSWER 2x3y

5. Find the ratio of the mass of the Milky Way galaxy, which is about 1044 grams, to the mass of the universe, which is about 1055 grams.

ANSWER 11011about

Homework Review

Practice for Quiz

EXAMPLE 1 Write numbers in scientific notation

4.259 107a. 42,590,000 =

b. 0.0000574 = 5.74 10-5

Move decimal point 7 places to the left.

Exponent is 7.

Move decimal point 5 places to the right.Exponent is – 5.

EXAMPLE 2 Write numbers in standard form

a. 2.0075 106 Exponent is 6.

Move decimal point 6 places to the right.

b. 1.685 10-4 Exponent is – 4.

Move decimal point 4 places to the left.

= 2,007,500

= 0.0001685

GUIDED PRACTICE for Examples 1 and 2

Write the number 539,000 in scientific notation. Then write the number 4.5 3 10 – 4 in standard form.

1. 539,000 5.39 105= Move decimal point 5 places to the left.

Exponent is 5.

4.5 10 – 4 = 0.00045 Exponent is – 4.

Move decimal point 4 places to the left.

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 10 , and 80,760,000 from least to greatest.

8

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 10 8 and 7.8 108. Because 1.034 < 7.8, you know that 1.034 108 is less than7.8 108.

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 10 4)– 1.6

= 10 3 –

1.21.6

10 4Product rule for fractions

(10 7)= 0.75

(7.5 10 1)– = 10 7

7.5 (10 1 – = 10 7)

(10 6)= 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

SOLUTION

STEP 1

Write each number in scientific notation, if necessary.

Order 2.7 × 10 5, 3.401 × 10 4, and 27,500 from least to greatest.

2.

27,500 = 2.75 × 104

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.

So, 2.7 104 < 2.7 105 < 3.401 104

GUIDED PRACTICE for Examples 3 and 4

Because 104 < 105, you know that 3.401 104, 0.7 104 is less than both 2.7 105. Because 2.7 < 3.401, you know that 2.7 104 is less than 3.401 104

Order numbers in scientific notation

EXAMPLE 3

STEP 3

Write the original numbers in order from least togreatest.

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 2(10 5)–= 1.32

(10 10)–= 1.69

Power of a product property

Power of a power property

10 2

4. 4.5 10 5

– 1.5 =

10 2 –

4.51.5

10 5Product rule for fractions

10 7= 3 Quotient of powers property

GUIDED PRACTICE for Examples 3 and 4

5. (1.1 107) (1.7 102)

4.62 109=

Commutative property andassociative propertyProduct of powers property

Evaluate the expression. Write your answer in scientific notation.

(1.1 1.7) (102 107)=

Solve a multi-step problem

EXAMPLE 5

BLOOD VESSELS

Blood flow is partially controlled by the cross-sectional area of the blood vessel through which the blood is traveling. Three types of blood vessels are venules, capillaries, and arterioles.

Solve a multi-step problem

EXAMPLE 5

a. Let r1 be the radius of a venule, and let r2 be the

radius of a capillary.Find the ratio of r1 to r2.What does the ratio tell you?

b.

Let A1 be the cross-sectional area of a venule, and let A2 be the cross-sectional area of a capillary. Find the ratio of A1 to A2 . What does the ratio tell you?

c. What is the relationship between the ratio of the radii of the blood vessels and the ratio of their cross-sectional areas?

10 2

10 3

1.05.0

= ––

Solve a multi-step problem

EXAMPLE 5

SOLUTION

The ratio tells you that the radius of the venule is twice the radius of the capillary.

a. From the diagram, you can see that the radius of the venule r1 is 1.0 millimeter and the radius of the capillary r2 is 5.0 millimeter.10 –3

– 10 2

= 0.2 101 = 2 =r2

r1 – 10 2

– 10 35.01.0

Solve a multi-step problem

EXAMPLE 5

b. To find the cross-sectional areas, use the formulafor the area of a circle.

=πr1

2

πr22

= r 1

2

r 22

r 1 r 2

2

=

22= = 4

Write ratio.

Divide numerator and denominator by .

Power of a quotient property

Substitute and simplify.

A 2

A1

Solve a multi-step problem

EXAMPLE 5

The ratio tells you that the cross-sectional area of the venule is four times the cross-sectional area of the capillary.

c. The ratio of the cross-sectional areas of the blood vessels is the square of the ratio of the radii of the blood vessels.

6. WHAT IF? Compare the radius and cross-sectional area of an arteriole with the radius and cross-sectional area of a capillary.

GUIDED PRACTICE for Example 5

SOLUTION

10 1

10 3

5.05.0

= –– = 1 102 = 100=r2

r1 – 10 1

– 10 35.05.0

The radius of the arteriole r1 is 5.0 10-1 mm and the radius of the capillary r2 is 5.0 10-3 mm.

The ratio tells you that the radius of the arteriole is 100 times the radius of the capillary.

Solve a multi-step problem

b. To find the cross-sectional areas, use the formula

for the area of a circle.

=πr1

2

πr22

= r 1

2

r 22

r 1 r 2

2

=

1002= = 104

Write ratio.

Divide numerator and denominator by p.

Power of a quotient property

Substitute and simplify.

A 2

A1

GUIDED PRACTICE for Example 5