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