PTYS 170A1 (Spitale)
Homework #1
8/23/2016
Scientific Method / Unit Conversions
1) Express the following in scientific notation:
a) 1
b) 0.000452
c) 56904
d) 5003.5
e) 10
2) Evaluate the following, expressing your answer in scientific notation:
a) 30×6000
b) 3×10 1×7×105
c) 5.68×10−4×1000
d) 1.3×10 8+1
e) 0.2×50000
0.5
f) 3.48×108
0.0001
3) Using the attached conversion chart, convert the given quantities into the appropriate MKS units.
a) 100 miles = b) 3.88 kilometers = c) 396033 centimeters = d) 10 AU = e) 328 feet = f) 500 grams = g) 44 pounds ~ h) 45 metric tons = i) 12 hours = j) 15 minutes = k) 50 pounds = l) 200 kilowatt­hours = m) 5000 calories = n) 1 kiloton of TNT = o) 500 megawatts = p) 0° Celsius = q) 32° Fahrenheit = 4) Consider the question of whether life exists elsewhere in the universe. a) What is your hypothesis (i.e. extraterrestrial life does / does not exist)?
b) On what do you base your hypothesis?
c) How might you test your hypothesis?
d) How would you disprove your hypothesis?
PTYS 170A1 (Spitale)
UNIT CONVERSIONS COMMON UNIT RELATIONS
a) Units of Length (SI unit: meter)
1 kilometer = 1000 meters
1 meter = 100 centimeters
1 meter = 1000 millimeters
1 mile = 1609 meters
1 meter = 3.28 feet
1 AU = 1.496 x 1011 meters
b) Units of Mass (SI unit: kilogram)
1 kilogram = 1000 grams
1 gram = 1000 milligrams
1 kilogram ~ 2.2 pounds 1 metric ton = 1000 kilograms
1 megaton = 106 ton = 109 kilograms
c) Units of Time (SI unit: second)
1 hour = 60 minutes
1 hour = 3600 seconds
1 year = 3.154 107 seconds
d) Units of Force (SI unit: Newton)
1 pound = 4.448 Newtons
1 dyne = 10­5 Newton
e) Units of Energy (SI unit: joule)
1 kilojoule = 1000 joules
1 megajoule = 1 x 106 joules
1 calorie = 4.184 joules
1 kilowatt­hour = 3.6 x 106 joules
1 erg = 10­7 joules
1 ton of TNT = 4.184 109 joules
f) Units of Power (SI unit: watt)
1 kilowatt = 1000 watts
1 gigawatt = 1 x 109 watts
1 horsepower = 745.7 watts
g) Units of Temperature (SI unit: Kelvin)
Fahrenheit (Tf) to Celsius (Tc): Tc = (5/9)*(Tf – 32) Celsius to Fahrenheit: Tf = ((9/5)*Tc) + 32 Celsius to Kelvin (K): K = Tc + 273.15
Basic Math Reference Sheet
--------------------------------------------------------------------------------------------------------------------------------------------------Order of Operation:
Examples:
PEMDAS
Parentheses
−3 2=9
Exponents
−3 2=−9
358−22
Multiply or Divide
=5
43
2
Add or Subtract
76×5 3=160
--------------------------------------------------------------------------------------------------------------------------------------------------Quadratic Formula:
−b ±b 2−4ac
Solve ax 2 bxc =0, a ≠0
x=
2a
--------------------------------------------------------------------------------------------------------------------------------------------------Arithmetic Operations & Fractions:
abac =a bc 
2 823=2 83=2×11=22
4 20 ×4
b ab
20 =
=10
a =
8
8
c c
1/2 1 4 4 2
a /b a d
=
= × = =
3/4 2 3 6 3
c /d b c
1030 10 30
ab a b
=  =515=20
= 
2
2
2
c
c c
8 1 8 431 32 3 35
a c adbc
 =
=
=
 =
3 4
34
12
12
b d
bd
--------------------------------------------------------------------------------------------------------------------------------------------------Exponents:
a 0 =1 , unless a=0
4 0 =1
0 0 =0
1 5
15
n m
n m
a a =a
3 3 =3 =3 6=729
2 15 15 −7  8
an
1
=2
=2 =256
=a n− m = m−n
m
27
a
a
n m
nm
2 3
2
10  =10 10 2 10 2 =10 6
a  =a
n
n n
ab =a b
3×10 2=3 2 10 2 =9×100=900
1
1
1
−n
−3
a = n
5 = 3=
a
5 125
--------------------------------------------------------------------------------------------------------------------------------------------------Manipulating Powers of 10: (specific case for exponent operations)
10n 10 m =10 nm
105 10 2 10−3 =10[ 52 −3 ]=10 4
n
10
10 7
=10 n −m
=10  7−12=10−5
m
10
10 12
10 n m=10nm
10 5 3=105x3=1015
1
1
−n
−4
10 = n
10 = 4
10
10
--------------------------------------------------------------------------------------------------------------------------------------------------Radicals:
1
1
 a= 2a=a 2
 16= 216=16 2 =4
n a=a n
n ab= n a n b
 32=325 =2
3
3
3
27 64= 27  64=34 =12
1
5
1
3215625=2 315625=5
mna=nma
Square Root Property:
If x 2 = p then x=± p
--------------------------------------------------------------------------------------------------------------------------------------------------Logarithm:
Definition
log 5 125=3 since 53 =125
y=logb  x  is equivalent to x=b y
Special logarithms
log  x=log 10  x  Common Log
ln x =log e x 
Natural Log
log b  b=1
logb 1=0
log b  xy=log b  xlog b  y
x
log b  =log b  x −log b y 
y
logbbx =x
where
e=2.718281828 …
log 10=1
log 1=0
log 3×5=log3 log5
2
log  =log 2−log 7
7
log 5 5 2 =2