1. 7-2 Powers of 10 and Scientific Notation Warm Up Lesson Presentation
Lesson Quiz
Holt Algebra 1

2. Warm Up
Evaluate each expression.
 1,000
 1,000
 100
 100
5. 104
6. 10–4
123,000
0.123
0.3
10,000
0.0001 1

3. Objectives Evaluate and multiply by powers of 10.
Convert between standard notation and scientific notation.

4. Vocabulary
scientific notation

5. The table shows relationships between several powers of 10.
Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left.

6. The table shows relationships between several powers of 10.
Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right.

8. Example 1: Evaluating Powers of 10
Find the value of each power of 10.
A. 10–6
B. 104
C. 109
Start with 1 and move the decimal point six places to the left.
Start with 1 and move the decimal point four places to the right.
Start with 1 and move the decimal point nine places to the right.
10,000
1,000,000,000

9. You may need to add zeros to the right or left of a number in order to move the decimal point in that direction.
Writing Math

10. Check It Out! Example 1
Find the value of each power of 10.
a. 10–2
b. 105
c. 1010
Start with 1 and move the decimal point two places to the left.
Start with 1 and move the decimal point five places to the right.
Start with 1 and move the decimal point ten places to the right.
0.01
100,000
10,000,000,000

11. If you do not see a decimal point in a number, it is understood to be at the end of the number.
Reading Math

12. Example 2: Writing Powers of 10
Write each number as a power of 10.
A. 1,000,000 B
C. 1,000
The decimal point is six places to the right of 1, so the exponent is 6.
The decimal point is four places to the left of 1, so the exponent is –4.
The decimal point is three places to the right of 1, so the exponent is 3.

13. Check It Out! Example 2
Write each number as a power of 10.
a. 100,000,000 b
c. 0.1
The decimal point is eight places to the right of 1, so the exponent is 8.
The decimal point is four places to the left of 1, so the exponent is –4.
The decimal point is one place to the left of 1, so the exponent is –1.

14. You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1.
Multiplying by Powers of 10

15. Example 3: Multiplying by Powers of 10
Find the value of each expression.
A  108
Move the decimal point 8 places to the right.
2,389,000,000
B. 467  10–3
4 6 7
Move the decimal point 3 places to the left.
0.467

16. Check It Out! Example 3
Find the value of each expression.
a  105
Move the decimal point 5 places to the right.
85,340,000
b  10–2
Move the decimal point 2 places to the left.

17. Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied.
The first part is a number that is greater than or equal to 1 and less than 10.
The second part is a power of 10.

18. Example 4A: Astronomy Application
Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.
Write Saturn’s diameter in standard form.
Move the decimal point 5 places to the right.
120,000 km

19. Example 4B: Astronomy Application
Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.
Write Saturn’s distance from the Sun in scientific notation.
Count the number of places you need to move the decimal point to get a number between 1 and 10.
1,427,000,000
1,4 2 7,0 0 0,0 0 0
9 places
Use that number as the exponent of 10.
1.427  109 km

20. Standard form refers to the usual way that numbers are written—not in scientific notation.
Reading Math

21. Check It Out! Example 4a
Use the information above to write Jupiter’s diameter in scientific notation.
143,000 km
Count the number of places you need to move the decimal point to get a number between 1 and 10.
5 places
Use that number as the exponent of 10.
1.43  105 km

22. Check It Out! Example 4b
Use the information above to write Jupiter’s orbital speed in standard form.
Move the decimal point 4 places to the right.
13,000 m/s

23. Example 5: Comparing and Ordering Numbers in Scientific Notation
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
Step 2 Order the numbers that have the same power of 10

24. Check It Out! Example 5
Order the list of numbers from least to greatest.
Step 1 List the numbers in order by powers of 10.
2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014, 4.5  1030
Step 2 Order the numbers that have the same power of 10

25. Example 6: Astronomy Application
Light from the Sun travels at about miles per second. It takes about 15,000 seconds for the light to reach Neptune. Find the approximate distance from the Sun to Neptune. Write your answer in scientific notation.
distance = rate  time
Write 15,000 in scientific notation.
Use the Commutative and Associative Properties to group.
Multiply within each group. mi

26. Check It Out! Example 6
Light travels at about miles per second. Find the approximate distance that light travels in one hour. Write your answer in scientific notation.
distance = rate  time
Write 3,600 in scientific notation.
Use the Commutative and Associative Properties to group.
Multiply within each group.

27. Example 7: Dividing Numbers in Scientific Notation
Simplify and write the answer in scientific notation
Write as a product of quotients.
Simplify each quotient.
Simplify the exponent.
Write 0.5 in scientific notation as 5 x
The second two terms have the same base, so add the exponents.
Simplify the exponent.

28. You can “split up” a quotient of products into a product of quotients:
Example:
Writing Math

29. Check It Out! Example 7
Simplify and write the answer in scientific notation.
Write as a product of quotients.
Simplify each quotient.
Simplify the exponent.
Write 1.1 in scientific notation as 11 x
The second two terms have the same base, so add the exponents.
Simplify the exponent.

30. Example 8: Application
The Colorado Department of Education spent about dollars in fiscal year on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.
To find the average spending per student, divide the total debt by the number of students.
Write as a product of quotients.

31. Example 8 Continued
The Colorado Department of Education spent about dollars in fiscal year on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.
To find the average spending per student, divide the total debt by the number of students.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The average spending per student is $5,800.

32. Check It Out! Example 8
In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt per person? Write your answer in standard form.
To find the average debt per person, divide the total debt by the number of people.
Write as a product of quotients.

33. Check It Out! Example 8 Continued
In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt per person? Write your answer in standard form.
To find the average debt per person, divide the total debt by the number of people.
Simplify each quotient.
Simplify the exponent.
Write in standard form.
The average debt per person was $12,800.

34. Lesson Quiz: Part I
Find the value of each expression. 1. 2.
3. The Pacific Ocean has an area of about 6.4 х 107 square miles. Its volume is about 170,000,000 cubic miles.
a. Write the area of the Pacific Ocean in standard
3,745,000
form.
b. Write the volume of the Pacific Ocean in scientific notation.
1.7  108 mi3

35. Lesson Quiz: Part II
Find the value of each expression.
4. Order the list of numbers from least to greatest

36. Lesson Quiz: Part III
5. The islands of Samoa have an approximate area of 2.9  103 square kilometers. The area of Texas is about 2.3  102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.

37. Lesson Quiz: Part IV
Simplify.
6. Simplify (3  1012) ÷ (5  105) and write the answer in scientific notation.
6  106
7. The Republic of Botswana has an area of 6  105 square kilometers. Its population is about 1.62  106. What is the population density of Botswana? Write your answer in standard form.
2.7 people/km2