Ch. 10: Mathematics Flashcards
what is the number before the x 10^y in scientific notation called? (3 names)
- significand
- coefficient
- mantissa
what types of numbers can the significand contain?
must be a number with an absolute value in the range [1,10)
func: significant figures
provide an indication of our certainty of a measurement and help us to avoid exceeding that certainty when performing calculations
what are the 4 parts of determining the number of significant figures in a number?
- count all numbers between the first nonzero digit on the left and the last nonzero digit on the right. Any digit between these two markers is significant
- any zeroes to the left of the first nonzero digit are considered leading zeroes and are not significant
- if there are zeroes to the right of the last nonzero digit and there is a decimal point in the number, then those zeroes are significant figures. If there is no decimal point, they are not significant.
- For measurements, the last digit is usually an estimation and is not considered significant.
When is it okay to round? When do you need to be more careful?
It is not okay to round when the answer choices are very close together, but when the answer choices are far apart it is ALL you need
For multiplication, how many decimal places is it generally acceptable to round to if the answer choices are close? if far away?
close: one decimal place!
far away: one sig fig
for multiplication, can you round both numbers up?
keep in mind whether the rounded number is larger or smaller than the original number
if one number is rounded up, it is best to round the other number down slightly to compensate
for multiplication, can you round both numbers up?
yes, unlike in multiplication, you should try to make proportional adjustments in the same direction
any number to the zeroth power equals what?
1
(X^0 = 1)
when multiplying two numbers with the same base, what can we do with the exponents?
X^a * X^b = X^(a+b)
you can add the exponents
when dividing two numbers with the same base, what can we do with the exponents?
X^a/X^b = X^(a-b)
you can subtract the exponents
for a number that is raised to an exponent and then raised again to another exponent, what can we do with the exponents?
(X^a)^b = X^(a*b)
you can multiply the exponents
when a fraction is raised to an exponent, what can we do with the exponents?
(X/Y)^a = X^a/Y^b
the exponent is distributed to the numerator and denominator
what do negative exponents represent?
inverse functions
X^(-a) = 1/(X^a)
how can fractional exponents be rearranged?
the numerator can be treated as the exponent and the denominator represents the root of the number
X^(a/b) = broot(x^a)
13 x 13
14 x 14
15 x 15
16 x 16
17 x 17
18 x 18
19 x 19
20 x 20
13 x 13 = 169
14 x 14 = 196
15 x 15 = 225
16 x 16 = 256
17 x 17 = 289
18 x 18 = 324
19 x 19 = 361
20 x 20 = 400
what are two methods for calculating the square root of any number less than 400?
- approximate its value by determining which two perfect squares it falls between
- you can divide the number given to you by known squares to attempt to reduce it
square root (2)
square root (3)
square root (2) = 1.4
square root (3) = 1.7
log(baseA) 1 = ?
log(baseA) 1 = 0
log(baseA) A = ?
log(baseA) A = 1
log A * B = ?
log A * B = log A + log B
log A/B = ?
log A/B = log A - log B
log A^B = ?
log A^B = B log A
log 1/A = ?
log 1/A = - logA
what is an aka for - log?
p!
defn: common vs. natural logarithms
common logarithms: base-ten logarithms
natural logarithms: based on Euler’s number (e, about 2.718)
conversion between natural and common logarithms
log x = lnx/2.303
what is a reasonable approximation of log (n * 10^m)?
log (n * 10^m) = m + 0.n
SOHCAHTOA
Sine = opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent
what is the range of values for sine and cosine? for tangent?
sine and cosine: -1 to 1
tangent: - infin to infin
direct vs. inverse relationships
DIRECT = increasing one variable proportionately increases the other (as one decreases, the other decreases by the same proportion)
INVERSE = an increase in one variable is associated with a proportional decrease in the other
tera-
10^12
T
giga-
10^9
G
mega-
10^6
M
kilo-
10^3
k
hecto-
10^2
h
deka-
10^1
da
deci-
10^-1
d
centi-
10^-2
c
milli=
10^-3
m
micro-
10^-6
u
nano-
10^-9
n
pico-
10^-12
p
how many feet are in a mile?
5280 ft
how many cm are in an inch?
2.54 cm
how many calories are in 1 Calorie?
1000 cal
how many joules are in 1 calorie?
4.184 J
how many joules are in an electron-volt?
1.602 * 10^-19 J
how many ounces are in a liter?
33.8 oz
how many newtons are in a lb?
4.45 N
how many kg are in one amu?
1.661 * 10^-27 kg
what is the conversion from celsius to fahrenheit?
F = (9/5)C + 32
what is the conversion from celsius to kelvin?
K = C + 273
func + aka: dimensional analysis
aka: unit analysis
func: a strategy to find an answer especially if you forget the equation
what are the 3 methods for solving systems of linear equations?
- substitution
- setting equations equal
- elimination (multiplying or dividing equations to match coefficients and then adding or subtracting the equations)
