Use Scientific Notation Warm Up Lesson Presentation Lesson Quiz

Warm-Up 1. Order the numbers 0.014, 0.1, 0.01 from least to greatest. ANSWER 0.01, 0.014, 0.1 2. 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 1 1011 about

Write the number in scientific notation. Example 1 Write the number in scientific notation. Move decimal point 7 places to the left. a. 42,590,000 = 4.259 107 Exponent is 7. Move decimal point 5 places to the right. b. 0.0000574 = 5.74 10-5 Exponent is – 5.

Write the number in standard form. Example 2 Write the number in standard form. a. 2.0075 106 = 2,007,500 Exponent is 6. Move decimal point 6 places to the right. b. 1.685 10-4 = 0.0001685 Exponent is – 4. Move decimal point 4 places to the left.

Guided Practice Write the number 539,000 in scientific notation. Then write the number in standard form. 4.5 10 – 4 539,000 5.39 105 = 4.5 10 – 4 = 0.00045

Example 3 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. 103,400,000 = 1.034 108 80,760,000 = 8.076 107

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

Guided Practice Order 2.7  105, 3.401  104, and 27,500 from least to greatest. 2. ANSWER 27,500; 3.401  104; 2.7  105

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

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

Guided Practice 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 =

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.

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?

Example 5 SOLUTION 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 = r2 r1 – 10 2 10 3 5.0 1.0 10 2 10 3 1.0 5.0 = – = 0.2 101 = 2 The ratio tells you that the radius of the venule is twice the radius of the capillary.

To find the cross-sectional areas, use the formula Example 5 b. To find the cross-sectional areas, use the formula for the area of a circle. = πr12 πr22 A 2 A1 Write ratio. = r12 r22 Divide numerator and denominator by . r1 2 r2 = Power of a quotient property 22 = = 4 Substitute and simplify. The ratio tells you that the cross-sectional area of the venule is four times the cross-sectional area of the capillary.

Example 5 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.

Guided Practice 6. WHAT IF? Compare the radius and cross-sectional area of an arteriole with the radius and cross-sectional area of a capillary. ANSWER The cross-sectional area of the arteriole is 104 times larger than the cross-sectional area of the capillary.

Lesson Quiz Write the number in scientific notation. 1. 100,500 ANSWER 105 1.005 2. 0.0203 ANSWER 2.03 10–2 3. Write 3.06 107 in standard form. ANSWER 30,600,000

Lesson Quiz The diameter of Mercury is about 4.9 103 kilometers. The diameter of Venus is about 1.2 104 kilometers. Find the ratio of the diameter of Venus to that of Mercury. Round to the nearest hundredth. 4. ANSWER about 2.45