Sig Figs, Errors, and Uncertainties

Question 1

why do we use sig figs?

Answer 1

any analytical measurement is not exact. so we have sets of rules that we follow so that the final answer is at a number that we can be sure of, as we can only read values to a certain confidence level.

Question 2

what are the 4 rules for determining sig figs?

Answer 2

1. any non zero number is important
2. any leading zeros, even after decimal places are not important
3. trailing zeros are important
   4.only the values before the scientific notation are relevant

Question 3

what are the 4 rules for rounding sig figs?

Answer 3

1. when the digit to the right of the last sig fig is >5, round up
2. when the digit to the right of the last sig fig is <5, keep the original value
3. when the digit to the right of the last sig fig is =5, round to the nearest even value
4. when the next value = 0, keep it the same, but if it doesn’t = 0, round up

Question 4

how do you use sig figs for adding and subtracting?

Answer 4

you add/subtract as normal, but you can only keep the same decimal place as your least certain number

Question 5

how do you use sig figs for multiplying and dividing?

Answer 5

the final answer should have as many sig figs as your value with the least amount of sig figs

Question 6

how do you use sig figs for log functions?

Answer 6

log(x)= 2.530, where 530=mantissa

x and mantissa need the same amount of digits

Question 7

what are the 3 types of error?

Answer 7

random, gross, and determinate errors

Question 8

define random error

Answer 8

these errors cannot be predicted or estimated, such as vibrations from walking. these are represented by experimental uncertainty.

Question 9

define determinate errors

Answer 9

these are systemic errors that can either be avoided or corrected and these affect results. examples are instrumental and error of the method.

Question 10

define gross errors.

Answer 10

these are from personal faults that occur in a lab, and these are hard to correct and often need to repeat the analysis. examples are reading a scale incorrectly or spilling solutions.

Question 11

define accuracy

Answer 11

degree of agreement between the measured values and the true value. (getting values close to the bullseyes all in the same range)

Question 12

define precision

Answer 12

degree of agreement between replicate measurements of the same quantity. (being able to get the bullseyes multiple times in a row)

Question 13

what are the 2 ways to express uncertainty?

Answer 13

absolute and relative uncertainty

Question 14

define absolute uncertainty

Answer 14

the margin of uncertainty associated with a measurement (+/- 0.002)

Question 15

define relative uncertainty

Answer 15

compares the size of absolute uncertainty to the size of its associated measurement

RU = absolute (+/-) /magnitude of measurement

%RU = same as above just x100%

Question 16

how do you calculate absolute uncertainties when there are several of them?

Answer 16

Ea = square root (e1^2 + e2^2 + e3^2…)

a=absolute

Question 17

how do you calculate the relative uncertainties when there are several of them?

Answer 17

%Er = sqaure root (%e1^2 + %e2^2 + %e3^2)

r= relative

Question 18

how many sig figs do i put for uncertainties?

Answer 18

the first digit of the absolute uncertainty is the last sig fig in the answer

ex.
0.09456 +/- 0.02
—-> Uncertainty starts at the second place, so the first number has to stop at the second decimal place (still follow rounding rules)
=0.09 +/- 0.02