Presentation on theme: "Uncertainty In Measurement"— Presentation transcript:
1 Uncertainty In Measurement Accuracy, Precision,Significant Figures, and Scientific Notation
2 ACCURACYA measure of how close a measurement comes to the accepted or true value of whatever is being measuredAccepted value is a quantity used by general agreement of the scientific community (usually found in a reference manual)
3 PRECISIONMeasure of how close a series of measurements are to one anotherMeasurements can:Be very precise without being accurateHave poor precision and poor accuracyHave good accuracy and good precision
4 ERROR Difference between experimental value and accepted value Do you recall what accepted value is?Ea = | Observed – Accepted |
5 PERCENT ERRORSince it is close to impossible to measure (through experimentation) anything and reach the accepted value, there must be some way to determine just how close you actually got – that is called percent error.Percent error is simply a mathematical formula.% Error = (Ea ÷ Accepted Value) ×100
7 SIGNIFICANT FIGURESMeasurement that includes all of the digits that are known PLUS a last digit that is estimated.
8 SIGNIFICANT FIGURE RULE #1 Every nonzero digit is significantExamples:24.7 meters has 3 significant figures0.473 meter has 3 significant figures714 meters has 3 significant figures245.4 meters has 4 significant figures4793 meters has 4 significant figures
9 SIGNIFICANT FIGURES RULE #2 Zeros between nonzero digits are significantExamples:7003 meters has 4 significant figures40.79 meters has 4 significant figuresmeters has 5 significant figures
10 SIGNIFICANT FIGURE RULE #3 Zeros appearing in front of nonzero digits are not significantExamples:0.032 meters has 2 significant figuresmeters has 1 significant figuremeters has 2 significant figures
11 SIGNIFICANT FIGURES RULE #4 Zeros at the end of a number and to the right of the decimal place are always significant.Examples:43.00 meters has 4 significant figures1.010 meters has 4 significant figures9.000 meters has 4 significant figures
12 SIGNIFICANT FIGURES RULE #5 Zeros at the end of a number but to the left of the decimal are not significant UNLESS they were actually measured and not rounded.To avoid ambiguity, use scientific notation to show all significant figures if measured amounts with no rounding.THIS IS A DIFFICULT RULE TO UNDERSTAND SO LET’S TALK FOR A BIT.
13 RULE #5 continued300 meters (actually measured at 299) has 1 significant figure, but 300. meters (actually measured at 300.) has 3 significant figures. The actual (not rounded) amount should be shown as 3.00 x 102 meters.The rounded 300 meters (299) can also be shown in scientific notation but with only 1 significant figure: 3 x 102 meters.
14 CALCULATIONS USING SIGNIFICANT FIGURES In all cases, round to the correct number of significant figures as the LAST step.Your final answer cannot be more precise than the measured values used to obtain it.Scientific notation is often helpful in rounding your final answer to the correct number of significant figures.
15 ADDITION/SUBTRACTION RULE Answers will always be reported with the same number of decimal places as the measurement with the least number of decimal places.Example: m m mThe “math” answer would be mHowever, the precise answer can only have one decimal place:369.8 m or x 102 m
16 ADDITION/SUBTRACTION EXAMPLES grams grams =gramsPrecise Answer would be or x 102 grams454 cm cm cm =cmPrecise Answer would be 656 or 6.56 x 102 cmmeters – m =mPrecise Answer would be or x 10-1 m2.321 L – L =LPrecise Answer would be or x 100 m
17 MULTIPLICATION/DIVISION RULE Round the final answer to the same number of significant figures as the measurement with the least number of significant figures.Example: 7.55 m x 0.34 m“Math” answer will be m2But, the precise answer will be 2.6 m2 because the measurement 0.34 m only has 2 significant figures.
18 MULTIPLICATION/DIVISION EXAMPLES 2.3 g/mL x mL =gPrecise answer would be 28 or 2.8 x 101 grams5.45 g/mL x mL =gPrecise answer would be 82.5 or 8.25 x 101 grams35.6 g / 2.3 mL =g/mLPrecise answer would be 15 or 1.5 x 101 g/mLg / 3.56 mL =g/mLPrecise answer would be 4.37 or 4.37 x 100 g/mL
19 MEASUREMENTS Writing them out! Scientific Notation: the product of two numbers; a coefficient and 10 raised to a power“Product”: means multiplicationCoefficient always has one digitfollowed by a decimal and then therest of the significant figures
20 Numbers to Scientific Notation To change any number to scientific notation, move the decimal point directly behind the very first digit, counting how many places you move. Look at these examples:36,000 meters = 3.6 x 104 meters: I moved the “understood” decimal 4 places to the left
21 245,000,000 buttons = 2.45 x 108 buttons: I moved the understood decimal 8 places to the left. 150. Grams = 1.50 x 102 grams: I moved the decimal 2 places to the left. Note: I also put a zero on the end of my scientific notation.These examples are all BIG numbers (or numbers greater than one) so the exponents are positive.
22 Numbers to Scientific Notation 0.036 meters = 3.6 x 10-2 meters: I moved the decimal 2 places to the right liters = 2.45 x 10-5 liters: I moved the decimal 5 places to the right
23 Small to Scientific Notation 0.150 Grams = 1.50 x 10-1 grams: I moved the decimal 1 place to the right. Note: I also put a zero on the end of my scientific.These examples are all small numbers (or numbers less than one) so the exponents are negative.
24 Work-out these problems in your notes: Determine the number of significant figures:1) 0.5026)2)7) x 103 8) 1000 x 10-33)4) x 1049) 1.295)10) x 10-3
25 Bell Ringer Please take out a sheet of paper and number down to 10 You will have 8 minutes
26 Bell Ringer To Scientific Notation: To decimal: 1) 3427 3.427 x 103 1) 3427 3.427 x 1036) 1.56 x 104156002)4.56 x 10-37) x 10-2 0.00568) x 10-13) 123,453x 1054) x 1029) x 10-3x 1055)10) x 103x 1062.59
27 Bell Ringer #2 Please take out a sheet of paper and number down to 10 You will have 8 minutes
28 Bell Ringer #2 To Scientific Notation: To decimal: 1) 4005 1) 4005 6) 4.58 x 1042)7) x 10-4 8) x 10-33) 25,5144) 814,5249) x 1035) 23,564.1210) x 103
29 Work-out these problems in your notes: Addition and subtraction rule1) 6.18 x 10-4 x 10-4 2) 9.10 x 103 + 2.2 x 106 3) x 1034) 4.25 x x 10-25) 2.34 x 106 + 9.2 x 106
30 Work-out these problems in your notes: Multiplication and Division rule1) 8.95 x 107/ 1.25 x 105 2) (4.5 x 102)(2.45 x 1010) 3) 3.9 x 6.05 x 4204) 14.1 / 5 5) (1.54 x 105)(3.5 x 106)