Chapter 1.5 Uncertainty in Measurement, Significant Figures

Question 1

Significant Figures

Answer 1

digits we record, both certain and uncertain

Question 2

Three rules to determine which digits are significant:

Answer 2

1. Make sure the # has a decimal point
2. Start LEFT, then move right until reaching the first NONZERO digit, then start counting
3. Count that ^ digit and all else to the right as significant
   * ALL digits are significant EXCEPT zeros used only to position the decimal point

Question 3

When 0’s end a number: If there is a decimal point & a zero before or after the decimal…?

Answer 3

If there is a decimal point & a zero before or after the decimal, they ARE significant

ex. 1.1300 = 5 sig figs
ex. 6400. = 4 sig figs

Question 4

When 0’s end a number: If there is NO Decimal point…?

Answer 4

There is NO Decimal point, the zeros are NOT Significant, UNLESS exponential notation clarifies the #

ex. 5300 L = 2 sig figs
ex. 5.3x10² = 2 sig figs
ex. 5.300x10³ = 4 sig figs

Question 5

When 0’s end a number: If there is a Terminal decimal point…?

Answer 5

There is a Terminal decimal point, the zeroes before and after ARE significant

ex. 500mL = 1 sig fig
ex. 500.mL = 3 sig figs

Question 6

Rules for Arithmetic Operations: Multiplication & Division

Answer 6

Answer has same # of Sig Figs as the # w/ the least # of Sig Figs

Question 7

Rules for Arithmetic Operations: Addition & Subtraction

Answer 7

Answer is rounded to have the same # Of Digits after the decimal as the quantity w/ the fewest Digits

Question 8

Rules for Rounding Off: Digit is MORE THAN 5

Answer 8

Increase the next number by 1

ex. 3 sig figs for 5.379 = 5.38

Question 9

Rules for Rounding Off: Digit is LESS THAN 5

Answer 9

The next number remains the same

ex. 3 sig figs for 0.2413 = 0.241

Question 10

Rules for Rounding Off: Digit IS 5

Answer 10

Next digit increases by 1 IF ODD, but remains the same IF EVEN

ex. 3 sig figs for 17.6500 = 17.6
ex. 3 sig figs 17.75 = 17.8
* if 5 is followed by 0, “DIGIT IS 5” rule applies
* if 5 is followed by non zeroes, “MORE THAN 5” rule applies

Question 11

Accuracy

Answer 11

how close each measurement is to the actual value

Question 12

Precision

Answer 12

how close the measurements in a series are to each other

Question 13

Systematic Error

Answer 13

values that are all either Higher or Lower than the actual value

Question 14

Random Error

Answer 14

values that are Higher AND Lower than the actual value