Scientific Notation and Significant Figures

A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

Accuracy Versus Precision Accurate and precise: The knife thrower is precise (the knives are closely placed to one another) and accurate (the knives are where he wants it).

Accuracy Versus Precision Neither accurate nor precise: The knife thrower has neither placed the knives close to each other (making it imprecise) nor placed them where he wanted them (making them inaccurate).

Accuracy Versus Precision Precise, but not accurate: The knife thrower is precise (the knives are closely grouped) but not accurate (they are presumably not where he wanted them).

B. Percent Error Indicates accuracy of a measurement your value accepted value

B. Percent Error A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

C. Significant Figures Indicates precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

C. Significant Figures Counting Sig Figs –Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500

, C. Significant Figures Counting Sig Fig Examples ,

C. Significant Figures Calculating with Sig Figs –Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g

C. Significant Figures Calculating with Sig Figs (con’t) –Add/Subtract - The # with the lowest place value determines the place of the last sig fig in the answer. – = – =

C. Significant Figures Calculating with Sig Figs (con’t) –Exact Numbers do not limit the # of sig figs in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

C. Significant Figures (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL 18.9g g g

Scientific Notation Used to convert BIG numbers into small usable numbers Must be used to keep calculation PRECISE

D. Scientific Notation Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. Places moved = exponent. –Large # (>1)  positive exponent Small # (<1)  negative exponent –Only include sig figs. 65,000 kg  6.5 × 10 4 kg

D. Scientific Notation 2,400,000  g kg 7  km 6.2  10 4 mm Practice Problems

D. Scientific Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

Questions? “You have to be precise. You have to be specific, but you want to be accurate. That is first and foremost. You want to be on top of the story, but words do matter.’’ Wolf Blitzer