11 Significant Figures 2 1 3 4 5 How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks.21345
12 Significant FiguresThe more marks the better we can estimate.Scientist always understand that the last number measured is actually an estimate12345
13 Significant Figures 1 2 3 4 5 How do we read the ruler? 4.5515 cm? We needed a set of rules to decide12345
14 Rules for Working with Significant Figures: Leading zeros are never significant. Imbedded zeros are always significant. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.Addition or Subtraction: The last digit retained is set by the first doubtful digit.Multiplication or Division: The answer contains no more significant figures than the least accurately known number.
15 Significant Figure Rules Rule #1: All real numbers (1, 2, 3, 4, etc.) count as significant figures.Therefore, you only have to be concerned with the 0Whether a 0 is significant or not depends on the location of that 0 in the number
16 Which zeros count?Rule #2: Zeros at the end of a number without a decimal point don’t count12400 g (3 sig figs)Rule #3: Zeros after a decimal without a number in front are not significant.0.045 g (2 sig figs)
17 Which zeros count? Rule #4: Zeros between other sig figs do count. 1002 g (4 sig figs)Rule #5: Zeroes at the end of a number after the decimal point do countg (6 sig figs)
18 Other Information about Sig Figs Only measurements have sig figs.A a piece of paper is measured 11.0 inches tall.Counted numbers are exactA dozen is exactly 12Being able to locate, and count significant figures is an important skill.
19 Learning CheckA. Which answers contain 3 significant figures? 1) cm 2) cm 3) 4760 cm B. All the zeros are significant in 1) mL 2) mL 3) x 103 mL C. 534,675 g rounded to 3 significant figures is 1) 535 g 2) 535,000 g 3) 5.35 x 105 g
20 Learning Check 1) 22.0 and 22.00 2) 400.0 and 40 In which set(s) do both numbers contain the same number of significant figures?1) and 22.002) and 403) and 150,0004) 63,000 and 2.15) and 1446) and 2000NONOYES- 2YES- 2NOYES-1
21 Learning CheckHow many sig figs in the following measurements? 458 g g 4850 g g g g343348
22 Next we learn the rules for calculations Unfortunately, there are different rules for addition and subtraction and for multiplication and division
24 Your answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point in the problem.WOW!!! What does that mean?
26 Another Example 27.96 mL + 6.6 mL 34.56 mL 34.6 mL If mL of NaOH is added to 6.6 mLof HCL, what is the total volume of your solution?First line up the decimal placesThen do the addingFind the estimated numbers in the problemThis answer must be rounded to the tenths place27.96 mLmL34.56 mLmL