1. Use Scientific Notation
Warm Up
Lesson Presentation
Lesson Quiz

2. 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

3. 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 =
Exponent is 7.
Move decimal point 5 places to the right. b. =
Exponent is – 5.

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

5. Guided Practice
Write the number 539,000 in scientific notation. Then write the number in standard form.
– 4
539,000 =
– 4 =

6. Example 3
Order 103,400,000, , and 80,760,000 from least
to greatest.
SOLUTION
STEP 1
Write each number in scientific notation, if necessary.
103,400,000 =
80,760,000 =

7. 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 is less than both and Because < 7.8, you know that is less than
So, < <
STEP 3
Write the original numbers in order from least to
greatest.
80,760,000; 103,400,000;

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

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

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

11. Guided Practice
Evaluate the expression. Write your answer in scientific notation. 3.
( ) – 2
(10 10) –
= 1.69
10 2 4. –
1.5
107
= 3 5.
( ) ( )
4.62
109 =

12. 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.

13. 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?

14. Example 5
SOLUTION a.
From the diagram, you can see that the radius of the venule r1 is millimeter and the radius of the capillary r2 is 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.

15. 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.

16. 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.

17. 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.

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

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