2 2 types of measurementQualitative-a non-numerical description of matter. (ex: red stone, heavy brick, hot steel) Quantitative- a numerical measure. It must include a number, followed by a unit. (ex: 2.14 grams, 49.6 ml, kg)
3 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
4 Why Is there Uncertainty? Measurements are performed with instrumentsNo instrument can read to an infinite number of decimal placesWhich of these balances has the greatest uncertainty in measurement?
5 Taking Measurements When taking measurements: Read to the smallest increment(mark) on the instrumentEstimate one digit past the smallest increment(mark)
6 Reading the Graduated Cylinder Liquids in glass and some plastic containers curve at the edgesChanging the diameter of the cylinder will change the shape of the curveThis curve is called the MENISCUS
7 Reading the Graduated Cylinder Your eye should be level with the top of the liquidYou should read to the bottom of the MENISCUS
8 Use the smallest increments to find all certain digits, then estimate 1 more digit. There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are…mL.
9 Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is0.8 mLThe volume in the graduated cylinder ismL.
10 ___mL 10 mL Graduated Cylinder What is the volume of liquid in the graduate?___mL
11 ___mL 25mL graduated cylinder What is the volume of liquid in the graduate?___mL
12 100mL graduated cylinder ____mL What is the volume of liquid in the graduate?____mL
13 Practice Reading the Graduated Cylinder What is this reading?___ ml
14 Practice Reading the Graduated Cylinder What is this reading?____ ml
15 Measuring Liquid Volume What is the volume of water in each cylinder?Images created atABCPay attention to the scales for each cylinder.
16 Reading a graduated cylinder All of the equipment below measures volume in mL but the scales for each are different.___mL___mL____mL
17 Reading a BuretOn the graduated cylinder, zero was at the bottom of the scale, with values increasing going up the cylinder. However, a buret has zero at the top with values increasing going down the scale. Determine the scale. Read at the bottom of the meniscus with your eye level with the liquid.____mL
25 Precision and Accuracy Accuracy how close a result is to its true value.Precision refers to the repeatability of results.Neither accurate nor precisePrecise but not accuratePrecise AND accurate
26 Types of ErrorError- the difference between a measurement and the accepted value.Random Error - measurement has an equal probability of being high or low.Systematic Error – a repeated error, often resulting from poor technique or incorrect calibration.
28 Scientific Notation In science, we deal with some very LARGE numbers: 1 mole =In science, we deal with some very SMALL numbers:Mass of an electron =kg
29 Imagine the difficulty of calculating the mass of 1 mole of electrons! kgx???????????????????????????????????
30 Scientific Notation:A method of representing very large or very small numbers in the form:M x 10nM is a number between 1 and 10n is the exponent
31 .987654321Step #1: Insert an understood decimal pointStep #2: Decide where the decimal must endup so that one number is to its leftStep #3: Count how many places you bouncethe decimal pointStep #4: Re-write in the form M x 10n
32 2.5 x 109The exponent is the number of places we moved the decimal.
33 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bouncethe decimal pointStep #4: Re-write in the form M x 10n
34 5.79 x 10-5The exponent is negative because the number we started with was less than 1.
35 Convert each standard number to scientific notation: 2000 g m m 6.55 s kg 71.9 ms 96.3 g 8999 cm m 450 g
36 Convert each to floating decimal form: 7.00 x 102 m 17 x 100 cm 2.22 x 10-4 cm 3.00 x 108 m/s 9.45 x 10-8 m 6.02 x 1023 atoms 4.00 x 103 g 8.75 x 10-1 m 5.99 x 10-5 kg 6.78 x 10-6 m
37 Significant Figures-all the digits that are known to be true.
38 Rules for Counting Significant Figures - Details Nonzero Digits(1-9) always count as significant figures.3456 has4 significant figures
39 Rules for Counting Significant Figures - Details Zeros- Leading zeros never count assignificant figures.has3 significant figures
40 Rules for Counting Significant Figures - Details Zeros- Captive zeros(sandwiched zeros) always count as significant figures.16.07 has4 significant figures
41 Rules for Counting Significant Figures - Details ZerosTrailing zeros are significant only if the number contains a decimal point.9.300 has4 significant figures
42 Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures. They tend to be numbers of indivisible objects.7 computersor1 inch = cm, exactly
44 Sig Fig Practice #1 1.0070 m 5 sig figs(0) 17.10 kg 4 sig figs(0) How many significant figures in each of the following & which is the estimated digit?m 5 sig figs(0)17.10 kg 4 sig figs(0)100,890 L 5 sig figs(9)3.29 x 103 s 3 sig figs(9)cm 2 sig figs(4)3,200,000 2 sig figs(2)
45 Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the answer equals the least number of sig figs used in the calculation.6.38 cm x 2.0 cm =12.76 13 cm2 (2 sig figs)
46 Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3g/cm34.22 g/cm30.02 cm x cmcm20.05 cm2710 m ÷ 3.0 sm/s240 m/slb x 3.23 ftlb·ft5870 lb·ft1.030 g ÷ 2.87 mLg/mL0.359 g/mL
47 Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement.6.8 g g = 18.7 g (3 sig figs)
48 Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g g76.27 g76.3 g0.02 cm cm2.391 cm2.39 cm713.1 L LL709.2 Llb lblblb2.030 mL mL0.16 mL0.160 mL