MEASUREMENTS. Significant Figures

Transcription

1 SIGNIFICANT FIGURES

2 MEASUREMENTS Significant Figures Every measured value, that you record on paper, reflects the precision of the measuring device used to obtain that value. Every calculated value that you record on paper reflects the accuracy of that value compared to a standard established by the scientific community.

3 MEASUREMENTS Rules for Assigning Sig.Figs 1. All non-zero integers are significant All leading zeros are insignificant

4 MEASUREMENTS 3. All captive zeros are significant All trailing zeros are significant only if the measured value contains a decimal point No decimal point **Estimated zeros are significant** 4.80 cm Decimal point

5 TIME TO CHEAT If the decimal point is PRESENT Draw an arrow through any zeroes, starting at the left of the number. Stop when you come to a non-zero digit. The digits you haven t drawn through are significant , Sig. Figs. 5 Sig. Figs.

6 MEASUREMENTS Determine the number of sig.figs in each of the following measured values: a e b f c. 500 g. 201 d h

7 PRACTICE WITH SIG. FIGS. How many significant figures are in the following numbers? ,000 12,000. 5,

8 MEASUREMENTS Determining the Precision of the Measuring Instrument *The last digit in any measured value is ALWAYS an estimate.* This tells your reader that the instrument used was precise to the ten-thousandth place grams The estimated digit

9 MEASUREMENTS All measurements must contain a number and a unit (more later). The precision of the instrument determines the number of significant figures in the measured value The last digit in any measured value is always an estimate.

10 MEASUREMENTS Quiz Determine the number of significant digits in each of the following measured values: a f b g c h d i e j

11 MEASURING Adding and Subtracting You may report your answer to the least number of decimal places as there are in the least precise measured value.

12 MANIPULATING SIG. FIGS. Addition and Subtraction The least precise number determines how many significant figures you have by place value

13 MEASUREMENTS Applications of Significant Figures Multiplication and Division You are only allowed to report your answer to the least number of significant digits as there are in the least precise measured value used to obtain the values used in the operation.

14 MANIPULATING SIG. FIGS. Multiplication and Division The number with the least amount of sig. figs. determines how many sig. figs. are in your answer x Sig. Figs. 2 Sig. Figs. 2 Sig. Figs! 3200

15 MEASUREMENTS

16 SCIENTIFIC NOTATION Expression! When a quantity is represented by a number multiplied by 10 to the appropriate power M x 10 n Examples 65,000 km = 6.5 x 10 4 km nm = 4.97 x 10-3 nm

17 MEASUREMENTS Temperature Conversions: C = K K 273 = C Convert the following: 39 o C K 217K o C

18 ACCURACY AND PRECISION

19 MEASUREMENTS Accuracy- How close a result comes to the true value (the real answer) Precision- the reproducibility of multiple measurements (how close your measurements are to themselves) Can you be precise in your measurements but not accurate?

20 ACCURACY AND PRECISION Actual Density of Zinc = 7.13 g/ml Student 1 Student 2 Student g/ml 6.49 g/ml 8.47 g/ml g/ml 6.51 g/ml 7.12 g/ml 7.15 g/ml 6.50 g/ml g/ml 7.11 g/ml g/ml 8.05 g/ml

21 MEASUREMENTS When making measurements, problem solving and doing experiments, we can never get a true answer. In other words, we cannot do things under perfect conditions; therefore there is room for error. The measurement of this error is the Percent Error Percent Error= accepted-observed x 100% accepted

22 MEASUREMENTS An experiment is performed to calculate the density of lead. The calculated value for the density of lead is g/ml. The accepted value for the density of lead is g/ml. Calculate and evaluate the percent error for this result.

23 MEASUREMENTS Percent Error = X 100% 3.5 %

24 MEASUREMENTS It is important to know that no measurement is absolutely certain, in other words, measurements have some degree of uncertainty. This uncertainty is why we always include the percent error in our results section.

25 DENSITY

26 DENSITY Density: D=m V How much stuff in how much space D H2O = 1 g/ml

27 PRACTICE What is the density of lead if its mass is g and its volume is 25 ml? What is the volume of iron if its density is 2.7 g/ml and its mass is 68 grams? What is the mass of copper if its volume is 5.0 L and its density is g/l?

28 MEASUREMENT AND PROBLEM SOLVING Ms. Thompson

29 SI UNITS

30 MEASURING The System International A system that standardizes measurements. Based upon seven base units and a system of prefixes used to describe the magnitude of the base unit.

31 MEASUREMENT Quantity Unit Symbol Length Meter m Mass Kilogram kg Time Second s Electric current Ampere Temperature Kelvin K Amount of substance Mole A mol Luminosity Candela cd

32 METRIC SYSTEM

33 METRIC SYSTEM You will need to know the prefixes for the metric system and how to convert between them King Henry Died.. Drinking Chocolate Milk Monday Night Kilo Hecto Deka.. Deci Centi Milli Micro Nano

34 SI PREFIXES Prefix Unit Abbreviation Meaning Kilo k 1,000 m = 1 km Hecto h 100 m = 1 hm Deka da 10 m = 1 dam 1 m Deci d 1 m = 10 dm Centi c 1 m = 100 cm Milli m 1 m = 1000 mm Micro μ 1 m = 1,000,000 μm Nano n 1 m = 1,000,000,000 nm

35 DIMENSIONAL ANALYSIS FACTOR LABEL METHOD

36 STEPS TO PROBLEM SOLVING Read problem Identify data Make a unit plan from the initial unit to the desired unit Select conversion factors Change initial unit to desired unit Cancel units and check Do math on calculator Give an answer using significant figures

37 FACTOR LABEL METHOD Using the Factor Label Method to Convert Units. How many grams are there in milligrams? 1 g = 1000 mg mg X = g

38 FACTOR LABEL METHOD How many centimeters are there in meters? 100 cm = 1 m m x = 9.10 cm

39 HOW MANY MINUTES ARE IN 2.5 HOURS? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

40 SAMPLE PROBLEM You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters X 1 dollar = 29 quarters

41 LEARNING CHECK A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b) 244 cm c) 24.4 cm

42 ONE-STEP PROBLEMS TO TRY kg = g cm = m ml = L mg = g cm = m

43 FACTOR LABEL METHOD How many deciseconds are there in milliseconds? = 1 s 10 ds 1 s = 1000 ms ms x X = ds

44 LEARNING CHECK How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x?? 1 day

45 SOLUTION Unit plan: days hr min seconds 1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min = 1.2 x 10 5 sec

46 WAIT A MINUTE! What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min

47 DIMENSIONAL ANALYSIS APPETIZERS Convert 3,500 millimeters to meters. 3,500 mm x 1m 1000 mm = 3.5 m Convert 2.0 years to days. 2.0 years x 365 days 1 year = 730 days Convert 36 inches to miles. 36 inches x 1 foot x 1 mile = 12 inches 5280 feet Convert the density of water from g/ml to kg/dl 1 g 1 ml x 1 kg 1000 g x 1000 ml 1 L x 1 L 10 dl 5.7 x 10-4 miles = 0.1 kg/dl

48 A PROBLEM TO TRY: How DO you measure a year? In daylights? Assuming there are (on average) 12 hours of daylight per day, how many hours of daylight are in 1.00 year? In cups of coffee? Ms. Smith is a Java Junkie. If she drinks 4 cups of coffee each day, how many cups of coffee does she have in 1.00 year? In minutes? Show me the calculations that say that there are 525,600. minutes in 1.00 year.

49 ENGLISH AND METRIC CONVERSIONS If you know ONE conversion for each type of measurement, you can convert anything! You must memorize and use these conversions: Mass: 454 grams = 1 pound Length: Volume: 2.54 cm = 1 inch L = 1 quart

50 LEARNING CHECK An adult human has 4.65 L of blood. How many gallons of blood is that? Unit plan: L qt gallon Conversions: 1 quart = L Your Setup: 1 gallon = 4 quarts

51 PROBLEMS TO TRY 1. How many inches are there in 45.6 cm? (2.54 cm = 1 inch) 2. How many centimeters are there in x 10-6 kilometers? 3. How many hours are there in years? 4. How many inches are there in 35 millimeters? 5. How many milliliters are in one cubic meter? (There are 1,000 L in 1 m 3 ) 6. How many miles are there in 3.44 x 10 8 inches? (0.61 mi = 1 km)

52 TIPS FOR SOLVING D.A. PROBLEMS Tip #1: Where are you going? Determine what units should be in your final answer. This will help you figure out where to start! A car travels 72mph on the highway, and gets a gas mileage of 29mpg. How many gallons will the car burn in 2.50 minutes of driving?

53 TIPS FOR SOLVING D.A. PROBLEMS Tip # 2: Where are you starting? Use the information about where you should end to determine where to start. Single unit Single Unit Double unit Double Unit The start must always be given to you in the problem. A car travels 72mph on the highway, and gets a gas mileage of 29mpg. How many gallons will the car burn in 2.50 minutes of driving? Single unit

54 TIPS FOR SOLVING D.A. PROBLEMS Tip #3: Mapping your course Using ratios given to you in the problem, and ratios that you already know, determine how to move (step by step) to your answer. The next ratio you use must have a common unit with the number before it. A car travels 72mph on the highway, and gets a gas mileage of 29mpg. How many gallons will the car burn in 2.50 minutes of driving? 2.50 mins. x 1 hour 60 mins. x 72 miles x 1 gal. = gal. 1 hour 29 miles

55 DEALING WITH TWO UNITS If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

56 SOLUTION Initial 8450 ft x 12 in. x 2.54 cm x 1 m 1 ft 1 in. 100 cm x 1 min x 60 sec = 2400 sec 65 m 1 min

57 WHAT ABOUT SQUARE AND CUBIC UNITS? Use the conversion factors you already know, but when you square or cube the unit, don t forget to cube the number also! Best way: Square or cube the ENITRE conversion factor Example: Convert 4.3 cm 3 to mm 3 ( ) = 4.3 cm 3 10 mm 3 1 cm 4.3 cm mm cm 3 = 4300 mm 3

58 LEARNING CHECK A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

59 SOLUTION 1000 cm 3 1 dm 3 ( ) = 1 dm 3 10 cm So, a dm 3 is the same as a Liter! A cm 3 is the same as a milliliter.

60 METRICS AND MEASUREMENT ANSWERS 1) 0.35 dl 2) 0.95 kg 3) 27.5 cm 4) 1 kl 5) 1 L 6) 4.5 g 7) 250 mm 8) 0.5 dag 9) 7.5 cm 10) 1.5 x 10 4 mg

61 FACTOR-LABEL WORKSHEET HW ANSWERS 1) 1.77 x 10-7 m 2) 260 min. 3) 12.0 lbs. 4) 1.59 x 10-5 km 5) 1.3 x 10 4 s 6) cm 7) min. 8) 3.15 x 10 7 s 9) km/s 10) km/hr