ScientificEngineeringNotation 1 Essay

Submitted By robreishac
Words: 695
Pages: 3

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
3

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.

4

Scientific Notation: Example #1
Example:
Express 5630 in scientific notation.

5

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.

6

Scientific Notation: Example #2
Example:
Express 0.000628 in scientific notation.

7

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

9

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.
10

Engineering Notation: Example #1
Example:
Express 16346000000 in engineering notation.

11

Engineering Notation: Example #1
Example:
Express 16346000000 in engineering notation.

Solution:
16346000000 = 16346000000.0 = 16.346 × 109
9 Moves

Note : Because the decimal point was moved to the left, the power of 10 is positive.

12

Engineering Notation: Example #2
Example:
Express 0.0003486 in engineering notation.

13

Engineering Notation: Example #2
Example:
Express 0.0003486 in engineering notation.

Solution:
0.0003486 =