Presentation on theme: "Significant Figures, and Scientific Notation"— Presentation transcript:
1 Significant Figures, and Scientific Notation The valid measurements or digits are called SIGNIFICANT!
2 When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.
3 Significant figures are all the digits in a measurement that are known with certainty plus a last digit thatmust be estimated.
4 Uncertainties of Measurements Accuracy is the degree of “exactness” to which the measurement quantity can be reproduced.
5 AccuracyIs the extent to which a measured value agrees with the standard value of the quantity.CALCULATORS DO NOT INCREASE THE ACCURACY!
6 Using Significant Figures reflects precision by estimating the last digit What is the certain measurement? (52 ml)What is the estimated measurement? (.8 ml)
7 The instrument determines the amount of precision of the data. What is the certain measurement here? (62.4 g)What is the estimated measurement here? (.00 g)
8 Error vs. Mistakes ERROR MISTAKES Mistakes are caused by PEOPLE Scientific errors are caused by INSTRUMENTSScientific measurements vary in their level of certaintyMistakes are caused by PEOPLEMisreading, dropping, or other human mistakes are NOT error
9 Significant Digits Nonzero digits are always significant All final zeros after the decimal point are significantZeros between two other significant digits are always significantZeros used solely for spacing the decimal point are not significant
10 Exact and Counting Numbers do not have significant digits
11 Exact numbers are important: they are infinitely valuable Exact numbers are important: they are infinitely valuable. Counting numbers come only in whole numbers.
12 There are rules for: multiplication/division addition/subtraction and combined equations
13 The answer can’t be more precise than the question Rules for multiplication/division The result has the same number of significant figures as the factor with the fewest significant figuresThe answer can’t be more precise than the question
14 The answer can’t be more precise than the question Rules for addition/subtraction The result has the same number of decimal places as the number with the fewest decimal placesThe answer can’t be more precise than the question
15 1. Do the functions in parenthesis 2. Note the number of significant digits in the question3. Perform the remainder of calculations4. Round the final answer
16 Calculations Addition/Subtraction Multiplication/Division The answer is based on the number with the fewest decimal pointsMultiplication/DivisionThe answer is based on the number with the fewest significant digits
17 Round only the final answer in a series of calculations
18 Now You Try It! Add 24.686 m +2.343 m + 3.21 m = ? Calculator says:3 decimals, 3 decimals and 2 decimalsSo 2 decimals it isAnswer is mMultiply 3.22 cm by 2.1 cmCalculator says3 sig figs, 2 sig figs So 2 it is!Answer is 6.8 cm2
19 Divide .005673 L by 2.1 L Calculator says 0.0027014286 4 sig figs and 2 sig figs2 it is!Answer is L
20 Scientific NotationIn chemistry we often use very large or very small numbersWe also have to pay attention to significant figuresScientific notation allows us to do both easily!
21 Scientific Notation is using powers of ten 1000 becomes1 X 10 3becomes1 X
23 How to do problems with scientific notation Ex. 4. 7 x 10 25 x 1 How to do problems with scientific notation Ex. 4.7 x x 1.9 xfirst do numbers: 4.7 x 1.9estimate as 5 x 2 = 10now do powers: x = 12so 10 x or 1.0 x 10 13
24 Calculators can help First, type in the number (ie 4.5) Then press 2nd Finally, press EE(above the comma)The number will displayas 4.5 E 13Read this as 4.5 x 10 13
25 Significant figures are easy when using scientific notation 2 Significant figures are easy when using scientific notation 2.3 x has 2 sig figs 3.7 x has 2 sig figs The placeholder zeros are eliminated for you!