ch 10 - mathematics Flashcards
how many significant numbers should an answer have
as many as the fewest amount of significant numbers in any one of the species in the question stem
any number to zeroth power
1
multiplication example with exponents and same base number
X^A x X^B = X^(A + B)
division with exponents and same base number
X^A/X^B = X^(A-B)
number raised to an exponent and raised to another
(X^A)^B = X^(AxB)
fraction raised to exponent
(X/Y)^A = (X^A)/Y^A
negative exponents
X^-A = 1/X^A
fractional exponents
numerator is treated as exponent and denominator is root of the number. X^(A/B) = X^A root of B of that number
square root of 2
about 1.414 or 1.4
square root of 3
about 1.732 or 1.7
log sub A x 1
0
log sub A x A
1
log A x B
log A + log B
log (A/B)
log A - log B
log A^B
B log A
log (1/A)
-log A
what is p shorthand for
-log (pH, pKa)
expression for K sub a
K sub a = ([H+][A-])/[HA]
common logarithms
base-ten logs (log sub 10)
natural logarithms
logs that are based on Euler’s number (about 2.718) (log sub e or ln)
conversion between natural logs and common logs
log x = (ln x)/2.303
example of approximating value of log
log (n x 10^m) = log (n) + log (10^m) = m + log (n); because n is number between 1 and 10 its log will be a decimal between 0 and 1 (log 1 = 0, log 10 = 1) the close n is to 1 the closer log n will be to 0.
example of log
find log (9.2 x 10^8) = 8 + 0.92 = 8.92 approx
sine
soh: sin theta = opposite/hypotenuse = a/c; values range from -1 to 1
cosine
cah: cosine theta = adjacent/hypotenuse = b/c; values range from -1 to 1
tangent
toa: tan theta = opposite/adjacent = a/b; values range from -infinity to infinity
special right triangles
30-60-90 and 45-45-90
sin 0 degrees
0
sin 30 degrees
1/2
sin 45 degrees
square root of 2/2
sin 60 degrees
square root of 3/2
sin 90 degrees
1
sin 180 degrees
0
cos 0 degrees
1
cos 30 degrees
square root of 3/2
cos 45 degrees
square root of 2/2
cos 60 degrees
1/2
cos 90 degrees
0
cos 180 degrees
-1
tan 0
0
tan 30
square root of 3/3
tan 45
1
tan 60
square root of 3
tan 90
undefined
tan 180
0
direct relationships
in math, these relationships are characterized by the increasing of one variable proportionally increasing the other
inverse relationships
an increase in one variable decreases the other
prefix tera
abbreviation T, factor of 10^12
prefix giga
abbreviation G, factor of 10^9
prefix mega
abbr M, factor of 10^6
prefix kilo
abbr k, factor of 10^3
prefix hecto
abbr h, factor of 10^2
prefix deka
abbr da, factor of 10^1
prefix deci
abbr d, factor of 10^-1
prefix centi
abbr c, factor of 10^-2
prefix milli
abbr m, factor of 10^-3
prefix micro
abbr fancy u (mu), factor of 10^-6
prefix nano
abbr n, factor of 10^-9
prefix pico
abbr p, factor of 10^-12
Fahrenheit to Celsius
F = (9/5)C + 32
Celsius to Kelvin
K = C = 273
