Scientific Notation Powers of
Ten
“Big” Numbers
“Small” Numbers
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
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
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.
Power of the Exponent
Power of the Exponent
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Positive Exponent
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Check Answer
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Negative Exponent
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
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
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
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
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
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
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
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