scientific notation. scientific notation: a short-hand way of writing large numbers or small numbers...
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Scientific Notation
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Scientific Notation
Scientific Notation: a short-hand way of writing large numbers or small numbers without writing all of the zeros.
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The Distance From the Sun to the Earth
93,000,000
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Step 1
• 1) Rewrite the number as a number less than 10 but at least 1.
9.3 is less than 10, but at least one
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• Write number without zeros
Then…..
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• Count how many places you moved decimal
• Make that your power of ten
Step 2
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•93,000,000 --- Standard Form
•9.3 x 107 --- Scientific Notation
Standard v Scientific
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Example 1
• Convert to Scientific Notation• Given: 289,800,000
• Use: 2.898• Answer:
Why is the exponent positive?
2. 898 x 108
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Practice Problem
1) 0.0985 = 9.85 x 10?
2) 64,100,000,000 = 6.41 x 10?
3) 0.00279 = 2.79 x 10?
4) 4,200,000 = 4.2 x 10?
Write in scientific notation. Decide the power of 10
9.85 x 10-2
6.41 x 1010
2.79 x 10-3
4.2 x 106
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More Practice Problems
1) 734,000,000 = ______ x 108
2) 0.00072 = ______x 10-4
3) 90,000,000,000 = _____ x 1010
On these, decide where the decimal will be moved.
1) 7.34 x 108 2) 7.2 x 10-4 3) 9 x 1010
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Complete Practice Problems
1) 50,000
2) 0.005
3) 802,000,000,000
Write in scientific notation.
1) 5 x 104 2) 5.0 x 10-3 3) 8.02 x 1011
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Scientific Notation to Standard Form
Step 1: Determine the sign of the power of 10.
Step 2: Move the decimal point according to the power of 10.
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Scientific Notation to Standard Form
3.4 x 105 in scientific notation
340,000 in standard form
3.40000 --- move the decimal
Example 1
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Example 2
• Convert to Standard Notation
• Given: 5.093 x 10-6
• Answer: (move 6 places to the right)
0.000005093
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Write in Standard Form
1) 6.27 x 106
2) 9.01 x 104
3) 5.98 x 10-3
4) 9.0 x 100