Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Warm­up Exercises
1. Write each number in scientific notation:
b. 3400
a. 39,000,000
d. 300,300
c. 1,209,000
2. Write each number in standard form:
b. 1.06 x 108
a. 9.2 x 104
d. 4 x 10‐7
c. 6.003 x 10‐11
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Lesson 46: Solving Problems Using Scientific Notation
To multiply numbers written in scientific notation, we multiply the coefficients to find the coefficient of the product. Then we multiply the powers of 10 by adding the exponents.
Steps:
Justification:
(1.2 x 106)(4x 108)
Given
(1.2 x 4)(106 x 108)
Assoc and Comm Properties
4.8 x 1014
Simplified
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
If the product is not in the proper form of scientific notation, we revise the product so that there is one digit to the left of the decimal point.
What are the rules of scientific notation?
Example: (7.5 x 104)(2 x 103)
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Example: Find each product
a. (1.2 x 105)(3 x 105)
b. (4 x 104)(5 x 105)
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
To divide numbers in scientific notation we divide the coefficients, and we divide the powers of 10 by subtracting the exponents.
4.8 x 106
4.0 x 103
( )( )
4.8 106
4.0 103
If the quotient is not in the proper form, we reposition the decimal point and change the exponent.
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Example: Light travels at a speed of about 300,000 km/s. An hour is 3600 seconds. Write both numbers in scientific notation. Then estimate the distance light travels in an hour using scientific notation.
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Example: Find the quotient of each:
a. 1.44 x 1012
1.2 x 108
b. 3 x 108
4 x 104
c. 7.5 x 106
2.5 x 106
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Example: Earth's average distance from the sun is about 150 million kilometers. Light travels at about 300,000 km/s. Express both in scientific notation and estimate how long it takes the sun's light to reach Earth.
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Lesson 46 Solving Problems with Scientific Notation.notebook
January 20, 2015
Homework: Lesson 46: a­l & 10­23
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