Download Units and Conversions

Units and Conversions
 American (English) system - yards, pounds, tons, seconds
 Metric system (SI)
o mks system => meter (m), kilogram (kg), second (s)
o Metric prefixes for each power of 10
Prefix
deci
centi
milli
micro
nano
pico
femto
atto
Abbreviation
d
c
m
m
n
p
f
a
Value
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
Prefix
decka
hecto
kilo
mega
giga
tera
Abbreviation
da
h
k
M
G
T
Value
101
102
103
106
109
1012
 American to SI conversions:
1m
=
39.37 in
1 km
=
0.6214 mi
1 kg
=
2.205 lb
1L
=
0.2642 gal
o How to convert
 We can multiply anything by 1 in an equation
 Conversion factors can be written as fractions that equal 1
 For Example: 7 = 7 , so 7 / 7 = 1
1m
=
39.37 in ,
…SO
1 m / 39.37 in =
1
OR…
39.37 in / 1 m =
1
 Example: Express 170 pounds in units of kg.
170 lbs x
1 kg
----------2.205 lbs
=
170 x 1
lbs x kg
----------- x ------------- =
2.205
lbs
o Try: Express 170 m/s in units of miles/hour.
77.1 kg
Scientific Notation
 Convenient way to write huge numbers that deal with the macrocosmic and
the microcosmic in Astronomy
o Write in powers of 10 => 101 = 10 & 10-2 = 1/100
o The exponent tells you how many times to multiply or divide by ten
o Written as:
 a.00 x 10n , where 'a' and 'n' are whole numbers
 100 = 1
 100 is written as 102, or 1 x 102
 Converting from normal to scientific notation
o Decimal moves right => negative exponent => 0.0304 = 3.04 x 10-2
o Decimal moves left => positive exponent => 3040 = 3.04 x 103
 Converting from scientific to normal notation
o Positive exponent => decimal moves right => 3.04 x 103 = 3040
o Negative exponent => decimal moves left => 3.04 x 10-2 = 0.0304
o Try: Convert 2,398,000 to scientific notation.
o Try: Convert 6.549 x 104 to normal notation.
 Adding and Subtracting with Scientific Notation
o Convert the numbers so the exponents are equal
o Then add or subtract the numbers in the front part of the notation
(6.7 x 109) + (4.2 x 109) = (6.7 + 4.2) x 109 = 10.9 x 109 = 1.09 x 1010
(4 x 108) - (3 x 106) = (4 x 108) - (0.03 x 108) = (4 - 0.03) x 108 = 3.97 x 108
o Try: (5.5 x 109) + (1.55 x 1010)
o Try: (6.2 x 108) - (2.0 x 107)
 Multiplication and Division with Scientific Notation
o Rearrange so you can multiply or divide the numbers in front of the
powers of ten, and add (for multiplication) or subtract (for division) the
exponents
(6 x 102) x (4 x 10-5) = (6 x 4) x (102 x 10-5) = 24 x 102-5 = 24 x 10-3 = 2.4 x 10-2
(9 x 108)
(9 x 108) / (3 x 106) = ----------- = (9/3) x (108/106) = 3 x 108-6 = 3 x 102
(3 x 106)
o Try: (8 x 107) x (5 x 10-5)
o Try: (4 x 108) / (6 x 108)
Significant Digits
 Numbers should be given to the greatest accuracy that they are known
 Write answers with as many decimal places as the number in the problem with
the least amount of decimal places
 Rules for Significant Digits
o All non-zero numbers are significant.
943 => 3
o Trailing zeroes after a decimal point are significant.
 9430 => 3
943.0 => 4
943.10 => 5
o Captive zeroes are significant.
4903 => 4
o Leading zeroes are not significant.
0001 => 1 0.005 => 1
o All measurements or any number with units must abide by these rules.
o Any counting number or number with no units is significant.
 5 = 5.000…
5 apples = 5.000…
o Examples: 2.3 + 4.71 = 7.0 (NOT 7.01)
Number Sig. Digits
Number
2998
4
.1
10
1
.0100
190
2
190.
0.001
1
190.0
0.001000
4
1459
0.010
2
459.000
Sig. Digits
1
3
3
4
4
6
Basic Geometry
 Dimensions of Circles and Spheres
o The circumference of a circle with radius R is 2πR
o The area of a circle of radius R equals πR2
o The surface area of a sphere of radius R is given by 4πR2
o The volume of a sphere of radius R is (4/3)πR3
 Measuring Angles - Degrees
o 3600 in a circle
o 60' (minutes) in one degree
o 60" (seconds) in one minute
Basic Trigonometry
 In a right triangle:
o The longest side, opposite the right angle is the hypotenuse (c)
o The side adjacent to the angle labeled θ is side (b)
o The side opposite to the angle labeled θ is side (a)
o Pythagorean Theorem: a2 + b2 = c2
o Trig functions:
 sin θ = a / c
 cos θ = b / c
 tan θ = a / b
c
a
θ
900
b
Basic Algebra
 You can move variables (unknowns) across an equals sign in an equation just
by moving them from the top on one side, to the bottom on the other
o Example: d = distance; v = velocity; t = time; a = acceleration
 d = vt , can be changed to
 v = at , can be changed to
=> t = d / v
=> t = v / a
OR v = d / t
OR a = v / t