evaluating algebraic expressions 4-5 scientific notation ns1.1 read, write, and compare rational...

Evaluating Algebraic Expressions

4-5 Scientific Notation

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

California Standards



Remember negative exponents must be fractions/decimals.

• 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 for positive or left for negative of the number in order to move the decimal point.

Rewrite in your notes in your words.



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

Notes



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

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Scientific notation. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.

Notes



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.

Notes



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.

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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.

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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.Notes



0002.7 Think: Move the decimal left 3 places.

2.7 10–3

B. 2.7 10–3

Write the number in standard form.

Additional Example 3: Reading Numbers in Scientific Notation

0.0027

Notes



2.870000000 Think: Move the decimal right 9 places.

A. 2.87 109

2.87 109



2,870,000,000

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000001.9 Think: Move the decimal left 5 places.

1.9 10 –5

B. 1.9 10–5



0.000019

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evaluating algebraic expressions 4-5 scientific notation ns1.1 read, write, and compare rational...

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