Page 1

Math You Need to Know

Chapter 1 Circuits

ENGR 1375

2 Types of Numbers

• Exact Numbers – Precise to the exact number of digits presented

• 12 eggs in a dozen, not 12.2

• Used in text in descriptions, diagrams, and examples

• Approximate Numbers – ANY measurement obtained in laboratory settings where

the exact value cannot be found.

• Analog scale, digital display with only 2 digits instead of 4 (or

more).

NOTE: When working with exact and approximate numbers, care must be

made to include the appropriate number of significant digits in the result –

sometimes results must be rounded off to accomplish this. Page 2

Page 3

Powers of 10

• Examples of Powers of 10

100 = 1 x 100 = 1

101 = 1x 101 = 10

104 = 1x 104 = 1000

10-4 = 1x 10-4 = 0.0001 =

10-1 = 1x 10-1 = 0.1 =

10-6 = 1x 10-6 = 0.000001 =

Recall that 10-n =

1

10n

1

106

1

104 1

10

Page 4

Multiplying by of Powers of 10 • Multiplication by powers of 10: add exponents

103 x 104 = 107 (3 + 4 = 7)

101 x 107 = 108

101/2 x 103/2 = 104/2 = 102

103 x 10-4= 10-1 102 x 10-3/2 = 101/2

• To multiply a decimal form by a factor of 10,

move the decimal point to the right by the factor

100.0 x 103 = 100000 (move decimal right 3 places)

.01 x 105 = 1000 (move decimal right 5 places)

34.56 x 104 = 345600 (move decimal right 4 places)

Page 5

Divide by of Powers of 10

• Divide by powers of 10: subtract exponents 104 ÷ 102 = 102 (4 minus 2 = 2)

105 ÷ 10-3 = 108 (5 minus -3 = 8)

105/3 ÷ 10-1/3 = 106/3 = 102

• To divide a decimal form by a factor of 10, move the decimal point to the left by the factor 100 ÷ 104 = 0.01 (move to the left 4 digits)

1000000 ÷ 105 = 10 (move to the left 5 digits)

23400 ÷ 103 = 23.4 (move to the left 3 digits)

.034 ÷ 102 = 0.0034 (move to the left 2 digits)

Page 6

Combine multiply and divide

• Add or subtract exponents as necessary

• Combined with numbers, calculate numbers and

exponents separately

103 x 10-4

10-2 x 105

103 x 105 x 102

102 x 105 x 101 = 10 (3+5+2) - (2+5+1) = 102

= 10 (3-4) - (-2+5) = 10(-1 -3) = 10-4

2.1x103 x 4x105 x 3.3x102

5 x102 x 1.2 x105 x 2.4x101 x 2.1 x 4 x 3.3

5 x 1.2 x 2.4 =

= 1.925 x 102

10 (3+5+2) - (2+5+1)

Page 7

Exponents taken to powers

• When exponents are taken to powers,

multiply exponent times power (103 )4 = 10(3x4) = 1012

(10-3 )2 = 10(-3x2) = 10-6

(101/2 )4 = 10(1/2x4) = 102

( )3 = = 10-9

103

1

109

1

Page 8

Scientific Notation

• To express any real number in scientific notation,

put it into the form m x 10n , where m (mantissa)

is 1 or greater and less that 10 (1 ≤ m < 10). The

power, n, can be any integer value.

• Examples of scientific and floating point notation

46 294 = 4.6294 x 104 - (you must get mantissa between 1 and 10)

Move decimal place left 4 places (divide by 104) and insert factor 104

More examples

100 000 = 1 x 105 Floating point notation: 1 x E5

0.002 35 = 2.35 x 10-3 Floating point notation: 2.35 x E-3

468. Joules = 4.68x 102 J Floating point notation: 4.68 x E2

Page 9

Engineering Notation • Similar to Scientific notation (m x 10n ), except n is a

factor of 3 (3, 6, 9, -3, -6, or 0) and m can be any

convenient number less than 1000 (m < 1000)

• Examples: 477 x 103 , 0.0255 x 10-3 , 25.5 x 10-6

• Note that the 2nd and 3rd are the same value

• Note that there are equivalent prefixes for engineering

notation- See Table 1.2 in book

– Examples: kilo : 103 , mega: 106 giga: 109

milli: 10-3 , micro (also µ) 10-6 , pico: 10-9

• ANYTIME you see a prefix, you can mathematically

replace it with its exponent equivalent! Examples:

– 5 milliAmp = 5 x 10-3 Amp, 4.1 MegaOhm = 4.1 x 106 Ohms

• Or conversely, 25.4 x 103 Volt = 25.4 kiloVolt

Page 10

Changing Powers

• Anytime you need to change the exponent to another

value, you must also change the matissa.

– The rule is that if you multiply the 10 exponent by a factor of 10,

then you must divide the mantissa by the same factor

– Ex: Change 0.0255 x 10-3 to new mantissa with a power of 10-6

divide 10-3 by 103 to get 10-6), then must multiply the mantissa by

103 (move the decimal right by 3 places).

0.0255 x 10-3 = 25.5 x 10-6

Move decimal to right 3

places (mult by 103)

Move decimal to left 3

places ( divide by 103)

Changing Powers Example

• Convert 1500 µs (10-6 s) to ks (103 s)

Page 11

1500 x 10-6 s = 0.0000015 x 103 s

Move decimal to right 9

places ( multiply by 109)

Move decimal to left 9

places ( divide by 109)