1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Order each set of numbers from least to greatest.
, 10 , 10 , 10 4 –2 –1
10 , 10 , 10 , 10 4 –1 –2
2. 8 , 8 , 8 , 8 2 –2 3
8 , 8 , 8 , 8 3 2 –2
3. 2 , 2 , 2 , 2 3 –6 –4 1
2 , 2 , 2 , 2 3 1 –4 –6
, 5.2 , 5.2 , 5.2 2 9 –1 –2
5.2 , 5.2 , 5.2 , 5.2 9 2 –1 –2

3. NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general.
California
Standards

4. Vocabulary
scientific notation

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

6. You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.

7. Additional Example 1: Multiplying by Powers of Ten
Since the exponent is a positive 4, move the decimal point 4 places to the right.
140,000
B. 3.6  10-5
Since the exponent is a negative 5, move the decimal point 5 places to the left.

8. Check It Out! Example 1
Multiply.
A. 2.5  105
Since the exponent is a positive 5, move the decimal point 5 places to the right.
250,000
B  10-3
Since the exponent is a negative 3, move the decimal point 3 places to the left.
0 10.2
0.0102

9. Powers of 10 are used when writing numbers in scientific notation
Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.

10. Additional Example 2: Writing Numbers in Scientific Notation
Write the number in scientific notation. A
Think: The decimal needs to move 3 places to get a number between 1 and 10.
7.09  10-3
Think: The number is less than 1, so the exponent will be negative.
So written in scientific notation is 7.09  10–3.

11. Additional Example 2: Writing Numbers in Scientific Notation
Write the number in scientific notation.
B. 23,000,000,000
Think: The decimal needs to move 10 places to get a number between 1 and 10.
2.3  1010
Think: The number is greater than 1, so the exponent will be positive.
So 23,000,000,000 written in scientific notation is 2.3  1010.

12. Think: The number is less than 1, so the exponent will be negative.
Check It Out! Example 2
Write the number in scientific notation. A
Think: The decimal needs to move 4 places to get a number between 1 and 10.
8.11  10 -4
Think: The number is less than 1, so the exponent will be negative.
So written in scientific notation is 8.11  10–4.

13. Check It Out! Example 2
Write the number in scientific notation.
B. 480,000,000
Think: The decimal needs to move 8 places to get a number between 1 and 10.
4.8  108
Think: The number is greater than 1, so the exponent will be positive.
So 480,000,000 written in scientific notation is 4.8  108.

14. Additional Example 3: Reading Numbers in Scientific Notation
Write the number in standard form.
A  105
1.35  10 5
Think: Move the decimal right 5 places.
135,000

15. Additional Example 3: Reading Numbers in Scientific Notation
Write the number in standard form.
B. 2.7  10–3
2.7  10–3
Think: Move the decimal left 3 places.
0002.7
0.0027

16. Write the number in standard form.
Check It Out! Example 3
Write the number in standard form.
A  109
2.87  10 9
Think: Move the decimal right 9 places.
2,870,000,000

17. Write the number in standard form.
Check It Out! Example 3
Write the number in standard form.
B. 1.9  10–5
1.9  10 –5
Think: Move the decimal left 5 places.

18. Additional Example 4: Comparing Numbers in Scientific Notation
A certain cell has a diameter of approximately 4.11  10-5 meters. A second cell has a diameter of 1.5  10-5 meters. Which cell has a greater diameter?
4.11  10-5
1.5  10-5
Compare the exponents.
4.11 > 1.5
Compare the values between 1 and 10.
Notice that 4.11  10-5 > 1.5  10-5.
The first cell has a greater diameter.

19. Check It Out! Example 4
A star has a diameter of approximately
5.11  103 kilometers. A second star has a diameter of 5  104 kilometers. Which star has a greater diameter?
5.11  103
5  104
Compare the exponents.
Notice that 3 < 4. So 5.11  103 < 5  104
The second star has a greater diameter.

20. Lesson Quiz
Write each number in standard form.
 104
17,200
 10–3
0.0069
Write each number in scientific notation.
5.3  10–3
5.7  107
4. 57,000,000
5. Order the numbers from least to greatest. T 2  10–4, 9  10–5, 7  10–5
7  10–5, 9  10–5, 2  10–4
6. A human body contains about 5.6  microliters of blood. Write this number in standard notation.
5,600,000