Math for Electronics7/29/2014

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sine and arcsine

log

tangent and arctangent

degree and radian

exponent

Sign change

engineering notation

square and squareroot

scientific notation

Floating point notation

Checking Calculator Use

1) Check -32 versus (-3)2 Make sure you are getting the desired sign for your problems.

2) Check and Note that should give you an error; remember what an error looks like.

3) Check log 100 You should get 2.

4) Check sin(180) Make sure you are in degree mode, if you don’t get 0.

5) Check arctan(1) You should get 45 degrees or .785398… radians

6) Check Note that you have to use ( ) around the top part of this to get the right answer which is 3.

7) Check You should get 13000 (floating notation), (scientific notation), and (engineering notation)

Different Math Symbols for Multiplication, Division, and Exponents

10^3

6E3

Greek Letters

Common Prefixes

tera- T 10 12 (trillion) Greekgiga- G 10 9 (billion) Greekmega- M 10 6 (million) Greek

myria- ma 10 4 (ten thousand) Greek

kilo- k 10 3 (thousand) Greek

hecto- h 10 2 (hundred) Greek

deca- da 10 1 (ten) Greekdeci- d 10 -1 (tenth) Latin

centi- c 10 -2 (hundredth) Latin

milli- m 10 -

3 (thousandth) Latin

myrio- mo 10 -4 (ten-thousandth) Greek

micro- μ 10 -6 (millionth) Greek

nano- n 10 -9 (billionth) Latin

pico- p 10 -12 (trillionth) Italian

Reciprocals in Generaland of Powers of 10

Find the reciprocals of the following. 6

102 2.3

Scientific versus Engineering Notation

Standard Form or Scientific Notation A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is written in standard form or with scientific notation, ex.

43712 = 4.3712x104  

0.036 = 3.6x10-2 

Engineering Notation Engineering notation is similar to scientific notation except that the power of ten is always a multiple of 3, ex.

43712 = 43.712 103 = 0.043712 106  

0.036 = 36x10-3 = 36000 10-6

Units used in engineering may be made smaller or larger with the use of prefixes, ex. 4.7 kJ = 4.7x103 J = 4700 J 8 MV = 8x106 V = 8000000 V (note that M is mega or the prefix meaning 106)

Scientific versus Engineering Notation

Any sites given in the class are recommended as excellent math websites for multiple types of math problems.

Here are the specific links for help with Scientific and Engineering Notation http://www.engineeringtoolbox.com/standard-form-scientific-engineering-notation-d_1801.html

http://www.purplemath.com/modules/exponent4.htm

http://www.mathsisfun.com/numbers/scientific-notation.html

Operation with Powers of 10

Note that this answer is also in Engineering Notation!

Operation with Powers of 10

Note that this answer is NOT in Engineering Notation! Change it to 80.0x106

Operation with Powers of 10

Note that this answer is also in Engineering Notation!

Operation with Powers of 10

Powers

The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the power.

(2.4 x 104)3 = (2.4)3 x 10(4x3) = 13.824 x 1012 = 1.3824 x 1013

(6.53 x 10-3)2 = (6.53)2 x 10(-3)x2 = 42.64 x 10-6 = 4.264 x 10-5

Roots

Change the exponent if necessary so that the number is divisible by the root. Remember that taking the square root is the same as raising the number to the one-half power.

Note that the first two answers were in Engineering Notation before they were converted to scientific notation! The last answer must be changed to 0.6x103.

Chapter 1 Formulas and the Math that Goes with Them

Q:charge(coulombs), V:volt (volts), I:current(amperes),G:conductance(siemens), R:resistance(ohms), T:time(seconds)

Chapter 1 Formulas and the Math that Goes with Them

We don’t necessarily need to know what a formula does to work with it.

For Example:

If I= find I for Q=6.35C and T=3s I= (how do you divide decimals?)

Did you get I≈2.117? What are the units?

I ≈ 6.35C/3s=2.117C/s In math, we write the units as being divided. In electronics you may have special units, as in this case, where C/s is amperes (A). Your electronics teacher will go over the details with units.

Chapter 1 Formulas and the Math that Goes with Them

You will want to be able to manipulate your formulas, so that you don’t have to memorize as many of them.

For Example: If I=Q/T, then you can rewrite the formula I= by multiplying both sides by T.

which simplifies to I or .

If you then divide both sides of by I, you have . This simplifies to T or T=Q/I.

So you know 3 equations if you memorize one: I=Q/T, T=Q/I

Chapter 1 Formulas and the Math that Goes with Them

Can you derive the two other equations from R=1/G?

Operations with Decimals

Find the following:

3.5 + 6.7

6.7-2.9

3.4(6.3)

8.06/2.6

Finding Common Percent Values

How do you calculate 20%, 10%, 5%, 2%, 1%, 0.5%, 0.25%, and 0.1% in your head?

For example, what is 10% of 340? “of” means multiply10%x340=0.10x340=34.0=34. Note that the decimal moved 1 place to the left to make the number smaller.

What is 10% of 620? 840? 120? 9600?

Finding Common Percent Values

How do you calculate 20%, 10%, 5%, 2%, 1%, 0.5%, 0.25%, and 0.1% in your head?

Since 10% of 340 is 34, we know that 5% is half that17. 20% would be twice 3468.

Finding Common Percent Values

How do you calculate 20%, 10%, 5%, 2%, 1%, 0.5%, 0.25%, and 0.1% in your head?

1% of 340 is 0.01(340)=3.4 (the decimal moved two places to the left),

then 2% is twice that6.8.

0.5% would be half of 3.41.7, and 0.25% would be half of 1.70.85.

Finally, 0.1% would be 1/10 of 3.40.34 (the decimal moved three places to the left).

Finding Common Percent Values

Calculate 20%, 10%, 5%, 2%, 1%, 0.5%, 0.25%, and 0.1% of 1200.