Scientific Notation
REMEMBER:
When you have a whole number the exponent is positive.
When you have a decimal the exponent is negative.
Examples:
STANDARD FORM
SCIENTIFIC NOTATION
Move the decimal 5 times to the right
3.1 x 105
134,500
Place the decimal between the 1 and 3, then
count the numbers after the decimal to get your
positive exponent
Move the decimal 7 times to the left
0.0065
7.3512 x 10-7
Place the decimal between the 6 and 5, then
count the numbers between the decimals to get
your negative exponent
2 x 108
300
1.5 x 10-8
2,156,100,000
What is the difference between Scientific Notation with positive exponents and negative exponents?
Scientific Notation with a
Scientific Notation with a
POSITIVE exponent
NEGATIVE exponent
Means move the decimal to the RIGHT
Means move the decimal to the LEFT
Think about the number line when converting from scientific notation to standard form. On a
number line negative numbers are to the left and positive numbers are to the right.
Express each number in scientific notation
To convert to scientific notation
• Place the decimal between the first two numbers (not zeros)
• If it is a whole number, count all the numbers after the decimal for your positive
exponent
• If it is a decimal, count all of the numbers between the decimal that you wrote and the
one that was already there for the negative exponent
1. 456,000,000,000
________________________
2. 0.00005
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3. 0.230
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4. 56,000,000
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5. 0.000023
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6. 0.000005
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7. 46,100,000,000
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8. 0.00017
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9. 0.23450
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10. 56,000,000,000
________________________
11. 0.0000123
________________________
Express each number in standard form.
To change numbers from scientific notation to standard form follow these directions.
•
•
•
•
Start at the decimal
If the exponent is positive move the decimal that many times to the right
If the exponent is negative move the decimal that many times to the left
Rewrite your final answer without all the swoops
12. 1.4 X 10 ⁻7
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13. 8.1 X 10 ⁻⁴
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14. 2.4 X 10⁻3
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15. 7.2 X 10 ⁻⁵
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16. 5.0 X 10³
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17. 7.5 X 10²
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18. 1.5 X 10⁻²
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19. 1.1 X 10 ⁻⁴
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20. 2.4 X 10 ⁻⁷
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21. 7.1 X 10³
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