1 Warm Up Problem of the Day Lesson Presentation2 Warm Up Order each set of numbers from least to greatest , 10, 10, , 10 1, 10 0, , 8, 8, 8 8 2, 8 0,...

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Warm Up Problem of the Day Lesson Presentation

Course 3

4-4 Scientific Notation Warm Up

Order each set of numbers from least to greatest.

1. 10 4, 10 –2, 100 , 10 –1 10–2, 10–1, 100, 104 2. 82, 8–2, 83 , 80 8–2, 80, 82, 83 3. 23 , 2–6 , 2–4, 21 2–6, 2–4, 21 , 23 4. 5.22, 5.29 , 5.2–1 , 5.2–2 5.2–2, 5.2–1, 5.22, 5.29 Course 3

4-4 Scientific Notation

Problem of the Day Explain which problems you can or cannot solve.

1) 24 x 26

2) 43 x 812

3) n9 x m1

4) t7 x t13

Can solve 1 and 4 because the bases are the same Course 3

Cannot solve 2 and 3 because the bases are not the same

4-4 Scientific Notation

Learn to express large and small numbers in scientific notation and to compare two numbers written in scientific notation.

Course 3

4-4 Scientific Notation

Vocabulary scientific notation: • is a shorthand way of writing large or small numbers by using a power of 10 • has to be a number between 1 and 10 •Example: 1.7 or 9.4

Course 3

4-4 Scientific Notation Examples of number written in standard notation, that are easier to work with if written in scientific notation. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across.

The length of these numbers in standard notation makes them awkward to work with. Course 3

4-4 Scientific Notation

To express any number in scientific notation: In standard notation the number of atoms in a quarter is 97,700,000,000,000,000,000,000 In scientific notation the number of atoms in a quarter is 9.77 1022

Course 3

4-4 Scientific Notation Hint when expressing any number in scientific notation:

A positive exponent means move the decimal to the right A negative exponent means move the decimal to the left.

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4-4 Scientific Notation Translating Scientific Notation to Standard Notation Write the number in standard notation.

1.35

105

1.35

10

1.35

100,000

5

135,000

105 = 100,000 Think: Move the decimal right 5 places.

Helpful Hint

A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Course 3

4-4 Scientific Notation Translating Scientific Notation to Standard Notation Write the number in standard notation.

2.01

104

20,100

Course 3

Think: Move the decimal right 4 places.

4-4 Scientific Notation Translating Scientific Notation to Standard Notation Write the number in standard notation.

2.7 2.7 2.7 2.7

10–3 10–3

1 1000 1000

0.0027 Course 3

10

–3

1 = 1000

Divide by the reciprocal. Think: Move the decimal left 3 places.

4-4 Scientific Notation

Write the number in standard notation. 2.87

109

2,870,000,000

Course 3

Think: Move the decimal right 9 places.

4-4 Scientific Notation

Write the number in standard notation. 1.9

10–5

0.000019

Course 3

Think: Move the decimal left 5 places.

4-4 Scientific Notation

Write the number in standard notation. 5.09

108

509,000,000

Course 3

Think: Move the decimal right 8 places.

4-4 Scientific Notation

Helpful Hint

A number less than 1 will have a negative exponent when written in scientific notation.

Course 3

4-4 Scientific Notation Translating Standard Notation to Scientific Notation Write 0.00709 in scientific notation. 0.00709 7.09 7.09

10

Think: The decimal needs to move 3 places to get a number between 1 and 10. Set up scientific notation.

Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative.

So 0.00709 written in scientific notation is 7.09 Check 7.09 Course 3

10–3 = 7.09

0.001 = 0.00709

10–3.

4-4 Scientific Notation Write 0.000811 in scientific notation.

0.000811 8.11

Think: The decimal needs to move 4 places to get a number between 1 and 10.

8.11 10 Set up scientific notation. Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. So 0.000811 written in scientific notation is 8.11

Check 8.11 Course 3

10–4 = 8.11

10–4.

0.0001 = 0.000811

4-4 Scientific Notation Life Science Application A certain cell has a diameter of approximately 4.11 x 10-5 meters. A second cell has a diameter of 1.5 x 10-5 meters. Which cell has a greater diameter? 4.11 x 10-5

1.5 x 10-5

10-5 = 10-5

Compare powers of 10.

4.11 > 1.5

Compare the values between 1 and 10.

4.11 x 10-5 > 1.5 x 10-5

The first cell has a greater diameter. Course 3

4-4 Scientific Notation A certain cell has a diameter of approximately 5 x 10-3 meters. A second cell has a diameter of 5.11 x 10-3 meters. Which cell has a greater diameter?

5 x 10-3

5.11 x 10-3

10-3 = 10-3

Compare powers of 10.

5 < 5.11

Compare the values between 1 and 10.

5 x 10-3 < 5.11 x 10-3

The second cell has a greater diameter. Course 3

4-4 Scientific Notation Lesson Quiz: Part I Write each number in standard notation.

1. 1.72 2. 6.9

104

17,200

10–3

0.0069

Write each number in scientific notation.

3. 0.0053

5.3

10–3

4. 57,000,000

5.7

107

5. Order the numbers from least to greatest. T 2 10–4, 9 10–5, 7 10–5

7 Course 3

10–5, 9

10–5, 2

10–4

4-4 Scientific Notation Lesson Quiz: Part II 6. A human body contains about 5.6 106 microliters of blood. Write this number in standard notation. 5,600,000

Course 3

Textbook pgs. 177 #’s 21, 23, 25, 27, 29, 37, 39, 40, 41, 43, 45, 46, 49, 57, 58

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