Evaluating Algebraic Expressions 4-5 Scientific Notation

Evaluating Algebraic Expressions

4-5 Scientific Notation

Scientific Notation



How do I write numbers in scientific How do I write numbers in scientific notation?notation?

How do I calculate with scientific How do I calculate with scientific notation?notation?

When would I use scientific notation?When would I use scientific notation?

Scientific Notation Scientific Notation Essential QuestionsEssential Questions



Vocabulary

scientific notation



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.



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.



A. 14 104

Multiply.

14.0 0 0 0Since the exponent is a positive 4, move the decimal point 4 places to the right.

Additional Example 1: Multiplying by Powers of Ten

140,000

B. 3.6 105

0 0 0 0 3.6Since the exponent is a negative 5, move the decimal point 5 places to the left.

0.000036



A. 2.5 105

Multiply.

2.5 0 0 0 0Since the exponent is a positive 5, move the decimal point 5 places to the right.

Check It Out! Example 1

250,000

B. 10.2 103

0 10.2Since the exponent is a negative 3, move the decimal point 3 places to the left.0.0102



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.



Additional Example 2: Writing Numbers in Scientific Notation

Think: The number is less than 1, so the exponent will be negative.

A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10.

7.09 103

Write the number in scientific notation.

So 0.00709 written in scientific notation is 7.09 10–3.



Additional Example 2: Writing Numbers in Scientific Notation

Think: The number is greater than 1, so the exponent will be positive.

B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10.

2.3 1010


So 23,000,000,000 written in scientific notation is 2.3 1010.




Think: The number is less than 1, so the exponent will be negative.

A. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10.

8.11 10 4


So 0.000811 written in scientific notation is 8.11 10–4.




Think: The number is greater than 1, so the exponent will be positive.

B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and 10.

4.8 108


So 480,000,000 written in scientific notation is 4.8 108.



1.35000

135,000

Think: Move the decimal right 5 places.

A. 1.35 105

1.35 105

Additional Example 3: Reading Numbers in Scientific Notation

Write the number in standard form.



0002.7 Think: Move the decimal left 3 places.

2.7 10–3

B. 2.7 10–3


Additional Example 3: Reading Numbers in Scientific Notation

0.0027



2.870000000 Think: Move the decimal right 9 places.

A. 2.87 109

2.87 109



2,870,000,000



000001.9 Think: Move the decimal left 5 places.

1.9 10 –5

B. 1.9 10–5



0.000019



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.

Additional Example 4: Comparing Numbers in Scientific Notation

Compare the values between 1 and 10.

The first cell has a greater diameter.

4.11 > 1.5

Notice that 4.11 10-5 > 1.5 10-5.



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.


The second star has a greater diameter.

Notice that 3 < 4. So 5.11 103 < 5 104

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Evaluating Algebraic Expressions 4-5 Scientific Notation