Warm Up 1. Evaluate 5 2 – 3 ANSWER – Evaluate ANSWER Simplify 6a6a –4 b 0. ANSWER 6 a 4 4. Simplify 8x 3 y –4 12x 2 y –3. ANSWER 2x2x 3y3y 5. Find the ratio of the mass of the Milky Way galaxy, which is about grams, to the mass of the universe, which is about grams. ANSWER about

Homework Review

Practice for Quiz

EXAMPLE 1 Write numbers in scientific notation a. 42,590,000 = b = 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 Exponent is 6. Move decimal point 6 places to the right. b Exponent is – 4. Move decimal point 4 places to the left. = 2,007,500 =

GUIDED PRACTICE for Examples 1 and 2 Write the number 539,000 in scientific notation. Then write the number – 4 in standard form , = Move decimal point 5 places to the left. Exponent is – 4 = 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 = ,760,000 = Order 103,400,000, , and 80,760,000 from least to greatest. 8

Order numbers in scientific notation 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 10 7 < 10 8, you know that is less than both and Because < 7.8, you know that is less than So, < <

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

Compute with numbers in scientific notation EXAMPLE 4 Evaluate the expression. Write your answer in scientific notation. a. ( )( ) ( ) ( )= = ( ) = (10 1 ) = 10 8 Commutative property and associative property Product of powers property Write in scientific notation. Associative property = Product of powers property

Compute with numbers in scientific notation EXAMPLE 4 b. ( ) – 2 (10 3 ) – 2 = (10 6 ) – = 2.25 Power of a product property Power of a power property (10 3 ) c. ( ) – 1.6 = 10 3 – Product rule for fractions (10 7 ) = 0.75 ( ) – = (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, × 10 4, and 27,500 from least to greatest ,500 = 2.75 × 10 4

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, < < GUIDED PRACTICE for Examples 3 and 4 Because 10 4 < 10 5, you know that , is less than both Because 2.7 < 3.401, you know that is less than

Order numbers in scientific notation EXAMPLE 3 STEP 3 Write the original numbers in order from least to greatest. 27,500; × 10 4, and 2.7 × 10 5

GUIDED PRACTICE for Examples 3 and 4 Evaluate the expression. Write your answer in scientific notation. 3. ( ) – 2 2 (10 5 ) – = (10 10 ) – = 1.69 Power of a product property Power of a power property – 1.5 = 10 2 – Product rule for fractions 10 7 = 3 Quotient of powers property

GUIDED PRACTICE for Examples 3 and 4 5. ( ) ( ) = Commutative property and associative property Product of powers property Evaluate the expression. Write your answer in scientific notation. ( ) ( )=

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 r 1 be the radius of a venule, and let r 2 be the radius of a capillary.Find the ratio of r 1 to r 2. What does the ratio tell you ? b. Let A 1 be the cross-sectional area of a venule, and let A 2 be the cross-sectional area of a capillary. Find the ratio of A 1 to A 2. 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 ?

= – – 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 r 1 is 1.0 millimeter and the radius of the capillary r 2 is 5.0 millimeter. 10 –3 – 10 2 = = 2 = r 2 r 1 – 10 2 –

Solve a multi-step problem EXAMPLE 5 b. To find the cross-sectional areas, use the formula for the area of a circle. = πrπr 1 2 πrπr 2 2 = r 1 2 r 2 2 r 1 r 2 2 = 2 = = 4 Write ratio. Divide numerator and denominator by . Power of a quotient property Substitute and simplify. A 2 A 1

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 = – – = = 100 = r 2 r 1 – 10 1 – The radius of the arteriole r 1 is mm and the radius of the capillary r 2 is 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. = πrπr 1 2 πrπr 2 2 = r 1 2 r 2 2 r 1 r 2 2 = == 10 4 Write ratio. Divide numerator and denominator by p. Power of a quotient property Substitute and simplify. A 2 A 1 GUIDED PRACTICE for Example 5