Scientific NotationSmall Numbers Scientific notation can also be used to write very small numbers...
Transcript of Scientific NotationSmall Numbers Scientific notation can also be used to write very small numbers...
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Scientific Notation Powers of
Ten
“Big” Numbers
“Small” Numbers
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Scientific notation is used when writing very large numbers
Large Numbers
1 gram of water contains 330,000,000,000,000,000,000,000
molecules of water
3.3 x 1023
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Small Numbers Scientific notation can also be used to
write very small numbers
The mass of one gold atom is 0.000 000 000 000 000 000 000 327 grams
3.27 x 10-22
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Powers of Ten In scientific notation, a number is written
as the product of two numbers: a coefficient and a 10 raised to a power.
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Power of the Exponent
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Power of the Exponent
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Positive Exponent
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Check Answer
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Negative Exponent
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Calculator
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Express the Following in Scientific Notation
1. 700 m
2. 38,000 m
3. 4,500,000 m
4. 685,000,000,000 m
5. 0.005 4 kg
6. 0.000 006 87 kg
7. 0.000 000 076 kg
8. 0.000 000 000 8 kg
………….7 x 102 m
………….3.8 x 104 m
………….4.5 x 106 m
…..….6.85 x 1011 m
………….5.4 x 10-3 m
……….6.87 x 10-6 m
………….7.6 x 10-8 m
………….8 x 10-10 m
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Express the Following as Standard Numbers
1. 3.6 X 104 s
2. 5.4 x 10-4 s
3. 5.06 x 103 s
4. 9.34 x 10-10 s
5. 103 s
6. 8 x 100 s
7. 8.3 x 10-13 s
8. 10-2 s
…………. 360,000 s
………….0.000 54 s
…………. 5060 s
….. 0.000 000 000 934 s
…………. 1,000 s
………. 8 s
….0.000 000 000 000 83 s
…………. 0.01 s
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Adding in Scientific Notation
2.70 X 107 + 15.6 x 106 = ?
2.70 X 107 Leave alone because 2.7 is a
value between 1 and 10
1.56 X 107
Move the decimal once to the
left and increase exponent by
value of 1
15.6 X 106
2.70 X 107 + 1.56 x 107 = 4.26 x 107
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Subtraction in Scientific Notation
3.2 x10-8 - 4.9 x 10-5 = ?
3.2 x 10-8 Leave alone because it’s the
larger exponent
0.0049 x 10-8 Move the decimal 3 places to
the left
4.9 x 10-5
3.2 x 10-8 - 0.0049 x 10-8 = 3.1951 x 10-8
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Add or Subtract the Following:
1. 5 x 10-5 + 2 x 10-5
2. 7 x 108 – 4 x 108
3. 9 x 102 – 7 x 102
4. 4 x 10-12 + 1 x 10-12
5. 1.26 x 104 + 2.5 x 103
6. 7.06 x 10-3 + 1.2 x 10-4
7. 4.39 x 105 – 2.8 x 104
8. 5.36 x 10-1 – 7.40 x 10-2
…………..7 x 10-5
…………..3 x 108
………….. 2 x 102
…………..5 x 10-12
…………..1.51 x 104
……….. 7.18 x 10-3
…………..4.11 x 105
………..4.62 x 10-1
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Multiplication in Scientific Notation
3.7 x 107 x 2.5 x 103 = ?
3.7 x 2.5 = 9.25 Multiply the
coefficients
107 + 103 = 1010 Add the exponents
3.7 x 107 - 2.5 x 103 = 9.25 x 1010
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Dividing in Scientific Notation
8.9 x 107 ÷ 4.5 x 10-3 = ?
8.9 ÷ 4.5 = 1.98 Divide the
coefficients
107 – 10-3 = 1010 Subtract the
exponents
8.9 x 107 ÷ 4.5 x 10-3 = 1.98 x 1010
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Multiply or Divide the Following:
1. 4 x 102 x 1 x 108
2. 2 x 10-4 x 3 x 102
3. 3 x 101 x 3 x 10-2
4. 1 x 103 x 1 x 10-1
5. 6 x 102 ÷ 2 x 101
6. 8 x 104 ÷ 4 x 101
7. 9 x 105 ÷ 3 x 10-1
8. 4 x 10-3 ÷ 2 x 10-2
…………..4 x 1010
…………..6 x 10-2
………….. 9 x 10-1
…………..5 x 102
…………..3 x 101
……….. 2 x 103
…………..3 x 106
………..2 x 10-1