Scientific Notation Notes

The Mall of America is Bloomington, Minnesota, is the largest shopping and entertainment center in the United States. The table shows two features of the mall.

Standard Abbreviated Product of a Product of a Form Form number and a number and a power of ten power of ten using exponents Number of Parking 13 thousand 13 x 1,000 Spaces Area of Mall (square feet) 4,200,000

 A number is in ______

when it is written as the product of a number and a power

of ten.

EXAMPLES: 60,000 = 6.0 x 104

3,500,000,000 = 3.5 x 109

 The number MUST be ______to 1

and ______10.

EXAMPLES: Circle the numbers written in scientific notation.

45.6 x 103 2.3 x 1024 333.7 x 102 5.6 x 1012

1 1. To write a number in STANDARD FORM you apply the order of operations: First, evaluate the power of ten and then multiply.

 A shortcut would be to move the decimal to the right the same amount of times as the ______of ten (or as the number of zeros.)

EXAMPLE: 5.2 x 104 = 5.2 x 10,000 5.2 x 104 = move the decimal point 4 places to the right 5.2 x 104 = 52,000

YOUR TURN: Write Each Number in Standard Form a. 7.2 x 104 b. 3.8 x 109 c. 1.0 x 108

2. To write a number in SCIENTIFIC NOTATION: First, move the decimal point to right of the first digit and then find the power of ten by counting the number of places moved.

EXAMPLE: Write 42,500 in scientific notation.  42,500 has to be put into a number that is between 1 and 10 The greatest place value is the ones place.  The decimal would have to be moved 4 times to get a number between 1 and 10.  Once you have a number between 1 and 10 you can get rid of the last zeros.

42,500 = 4.2500 x 10,000 = 4.2500 x 104 = 4.25 x 104

2 YOUR TURN: Write each number in scientific notation.

23,500,000 = ______

38,000,000 = ______

19,000 = ______

86.1 billion = ______

WRITING: Explain why scientific notation is used with large numbers.

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NUMBER SENSE: Which number describes the population of Chicago, 3.0 x 106 or 3.0 x 103? Explain your reasoning.

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PLANETS: The average distance between Earth and the Sun is 92,960,000 miles. Write this distance in scientific notation.

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