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Flashcards in ch 10 - mathematics Deck (61)
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1

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

2

any number to zeroth power

1

3

multiplication example with exponents and same base number

X^A x X^B = X^(A + B)

4

division with exponents and same base number

X^A/X^B = X^(A-B)

5

number raised to an exponent and raised to another

(X^A)^B = X^(AxB)

6

fraction raised to exponent

(X/Y)^A = (X^A)/Y^A

7

negative exponents

X^-A = 1/X^A

8

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

9

square root of 2

about 1.414 or 1.4

10

square root of 3

about 1.732 or 1.7

11

log sub A x 1

0

12

log sub A x A

1

13

log A x B

log A + log B

14

log (A/B)

log A - log B

15

log A^B

B log A

16

log (1/A)

-log A

17

what is p shorthand for

-log (pH, pKa)

18

expression for K sub a

K sub a = ([H+][A-])/[HA]

19

common logarithms

base-ten logs (log sub 10)

20

natural logarithms

logs that are based on Euler's number (about 2.718) (log sub e or ln)

21

conversion between natural logs and common logs

log x = (ln x)/2.303

22

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.

23

example of log

find log (9.2 x 10^8) = 8 + 0.92 = 8.92 approx

24

sine

soh: sin theta = opposite/hypotenuse = a/c; values range from -1 to 1

25

cosine

cah: cosine theta = adjacent/hypotenuse = b/c; values range from -1 to 1

26

tangent

toa: tan theta = opposite/adjacent = a/b; values range from -infinity to infinity

27

special right triangles

30-60-90 and 45-45-90

28

sin 0 degrees

0

29

sin 30 degrees

1/2

30

sin 45 degrees

square root of 2/2