Scientific & Engineering
Notation
Digital Electronics
Scientific & Engineering Notation
This presentation will demonstrate…
• How to express numbers in scientific notation.
• How to express numbers in engineering notation.
• How to express numbers in SI prefix notation.
2
Scientific Notation
• Scientific notation is a way of writing very large and very small numbers in a compact form.
• A number written in scientific notation is written in the form: a × 10b
Where: a is a number greater than 1 and less than 9.99 b is an integer
Examples:
3.24 × 105
1.435 × 10-7
3.29× 106
7.3 × 10−2
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Writing A Number in Scientific Notation
• Shift the decimal point so that there is one digit
(which cannot be zero) before the decimal point.
• Multiply by a power of 10, equal to the number of places the decimal point has been moved.
• The power of 10 is positive if the decimal point is moved to the left and negative if the decimal point is moved to the right.
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Scientific Notation: Example #1
Example:
Express 5630 in scientific notation.
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Scientific Notation: Example #1
Example:
Express 5630 in scientific notation.
Solution:
5630 = 5630.0
= 5.630 × 103
3 Moves
Note: Because the decimal point was moved to the left, the power of 10 is positive.
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Scientific Notation: Example #2
Example:
Express 0.000628 in scientific notation.
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Scientific Notation: Example #2
Example:
Express 0.000628 in Scientific Notation.
Solution:
0.000628 = 6.28 × 10-4
4 Moves
Note: Because the decimal point was moved to the right, the power of 10 is negative.
8
Engineering Notation
• Engineering notation is similar to scientific notation. In engineering notation the powers of ten are always multiples of 3.
• A number written in engineering notation is written in the form: a × 10b
Where: a is a number greater than 1 and less than 999 b is an integer multiple of three
Examples:
71.24 × 103
4.32 × 10-6
320.49× 109
123.452 × 10−12
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Writing A Number in Engineering Notation
• Shift the decimal point in “groups of three” until the number before the decimal point is between 0 and 999.
• Multiply by a power of 10 that is equal to the number of places the decimal point has been moved. • The power of 10 is positive if the decimal point is moved to the left and negative if the decimal point is moved to the right.
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Engineering Notation: Example #1
Example:
Express 16346000000 in engineering notation.
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Engineering Notation: Example #1
Example:
Express 16346000000 in engineering notation.
