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Unit 2: Measuring and Calculating

Unit 2: Measuring and Calculating. “1000 grams...well it sounded like a lot when i orderd it. ah well, I cant make hide nor hair of these metric boobytraps”. Chapter 2. My car gets fourty rods to the hogshead and that's the way I like it. Objectives.

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Unit 2: Measuring and Calculating

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  1. Unit 2: Measuring and Calculating “1000 grams...well it sounded like a lot when i orderd it. ah well, I cant make hide nor hair of these metric boobytraps” Chapter 2 My car gets fourty rods to the hogshead and that's the way I like it

  2. Objectives • By the end of this unit, you will be able to: • Distinguish between qualitative and quantitative characteristics • List three requirements for making a measurement • List and define the seven basic SI units with their categories of measurement • Define the commonly used SI prefixes • Define mass, weight, balance, and state the difference between mass and weight • Define temperature and give the basis for the Celsius temperature scale • Distinguish accuracy and precision

  3. Objectives cont. • Define significant digits and counting numbers and determine the number of significant digits in a given measurement • Express results of math equations in significant digits • Convert numbers from decimal to scientific notation • Combine SI units to form derived units • Demonstrate use of logic to solve problems • Use the factor-label method to solve problems • Define density and perform calculations using density, mass, and volume

  4. The International System (SI) • Qualitative measurement – a description with no measurement • Color • Smell • Quantitative measurement- a description with numerical information • Length • Mass

  5. SI System continued… • Three requirements for quantitative measurement • We must know exactly what property we are trying to measure • We must have some standard with which to compare whatever we are measuring • We must have some method of making this comparison

  6. SI System continued… • The SI system is the standard measuring system used in science • SI is a modified version of the metric system • Most countries use SI or are converting to it • The SI system is very simple and consistent • The SI system has seven basic units…

  7. Seven Basic Units of SI

  8. SI prefixes • In SI, prefixes are added to the base units to obtain different units of a convenient size for measuring larger or smaller quantities • Kilometer = 1000 meters • Millimeter = 1/1000 of a meter • You will need to memorize the metric prefixes and the values which they stand for • Next, a table of the metric prefixes…

  9. SI Prefixes

  10. Homework • Worth a possible 5 points • Due:

  11. Mass and Weight • What's the difference? • Weight is a measure of the force of gravity between two objects • On objects weight on Earth can change when the distance between the object and the center of the Earth changes • Mass is a measure of the amount of matter an object has • Mass never changes

  12. Mass • The SI unit for mass is the kilogram • In the lab, we usually use the gram (g), because a kilogram is too large • The mass of a paperclip is about 1.5 g • The Balance • The balance is the tool used to measure mass • Using the balance

  13. Length • Length is the distance covered by a line segment connecting two points • The SI unit for length is the meter (m) • Length is usually measured with a ruler or similar device • Examples • A nickel has a diameter of ~2 cm • A notebook is about 25 cm long

  14. Time • Time is the interval between two occurrences • The SI unit for time is the second (s) • Time is usually measured with a clock or watch • The atomic clock is the most accurate tool for measuring time

  15. Temperature • The temperature of a sample of matter is a measure of the average kinetic energy of the particles that make up the sample • The greater the kinetic energy, the higher the temperature • Temperature is usually measured with a thermometer • The SI unit for temperature is the Kelvin (k) • The Celsius scale is also often used • The Celsius scale is based on the boiling point and freezing point of water • It is related to the Kelvin scale. More later…

  16. Accuracy Vs. Precision • Accuracy refers to how close a measurement is to the true or correct value for the quantity • Precision refers to how close a set of measurements for a quantity are to one another, regardless of whether the measurements are correct • Usually measurements that have precision are also accurate, but not always

  17. Assignment • Complete Exercises 1-2 on page 19 of your text • Complete Exercises 3-4 on page 23 of your text • This assignment is worth 10 points • Due: By the end of class

  18. Significant Digits (Sig Fig’s) • All digits that occupy places for which actual measurement was made are referred to as significant digits • The places actually measured include one uncertain, or estimated digit • See Figure 2-7 in your text

  19. Sig Fig’s cont. • The exactness of measurements is very important • This is determined by the number of significant digits in the measurement • There are a few rules for determining the number of significant digits in a recorded measurement • Counting numbers (an exception) • When something is counted (not measured) it is considered to have an infinite amount of significant figures (more on that later)

  20. Sig Fig Rules • Digits other than zero are always significant • 96 g 2 sig figs • 61.4 3 sig figs • 0.52 2 sig figs • One or more final zeros used after the decimal point are always significant • 4.7200 km 5 sig figs • 8.0 2 sig figs • Zeros between two other significant digits are always significant • 5.029 m 4 sig figs • Zeros used solely for spacing the decimal point are not significant • 7000 g 1 sig fig • 0.00783 kg 3 sig figs

  21. Practice • How many significant digits in each of the following? • 30.4 • 2700 • 5.10 • 0.023 • 7.0200 • 0.04010 • 3.00 • 2.700 • 0.0304 • 51.0

  22. Assignment • Complete Exercise 5 on page 24 of your text • This assignment is worth 5 points • Due: Tomorrow

  23. Pop Quiz!!! • Write the correct number of sig figs for the following: 1. 320 g 11. 1234 meters 2. 32.0 m 12. 100,000 cd 3. 0.0045 kg 13. 504.0032 g 4. 50,000.0 L 14. 9.8 km 5. 2.340 cm 15. 100.0001 pm 6. 756 dm 16. 300 g 7. 100 g 17. 5.34 ML 8. 0.000500 L 18. 34 L 9. 1.096 mL 19. 0.001 g 10. 11.506 cg 20. 50 pencils

  24. Scientific Notation • Scientific Notation makes it easier to work with large numbers • In Scientific Notation all numbers are expressed as the product of a number between 1 and 10 and a whole-number power of 10 • M x 10n • 1,000 = 1 x 103 • Using Scientific Notation also makes counting sig figs easier • 8000 = 8 x 103 1 sig fig • 8000.0 = 8.0000 x 103 5 sig figs

  25. Scientific Notation Practice • Convert the following to scientific notation • 30,000 • 1,567 • 0.000000340 • 5.67 • 7,500,000

  26. Scientific Notation Rules • To determine the number of digits that should appear in the answer to a calculation, we use two rules • In addition and subtraction, the answer may contain only as many decimal places as the measurement having the least number of decimal places • 5.44 + 3.1 = 8.5 • This answer should then be rounded off to the nearest tenth, so the answer would be 8.5 • In Multiplication and division, the answer may contain only as many significant digits as the measurement with the least number of significant digits • 1.1 x 2.000 = 2.200 • You can only have 2 significant digits, so your answer would be 2.2

  27. Assignment • Complete Exercises 6-12 on page 27 of your text • This will be worth a possible 10 points • Due: Tomorrow

  28. Derived Units • By combining SI units, we can obtain measurement units to express other quantities • Distance divided by time = speed • Length x Length = area • Unit of area is the square meter (m2) • Area x Length = volume • Unit of volume is the cubic meter (m3) • Most often in lab we use the milliliter (mL) for volume • 1000 cm3 = 1000 mL = 1 L = 1 (dm3)

  29. Problem Solving • 3 part method for solving problems • Decide what information is given • Decide what information is needed • Find a “bridge” that can help you use the information that you have to obtain the information that you need • The “bridge” is the information that you will learn studying chemistry

  30. Conversion Factors • A conversion factor is a ratio equivalent to one • Convert 72 cm to meters • 100 cm = 1 meter • 100 cm/100cm = 1m/100cm; therefore 1m/100cm is your conversion factor • 72cm x 1 = 72cm x (1m/100cm) • So, 72cm = 72m/100 = 0.72 m • Convert 5.5 L to ml

  31. Conversion Factors Cont. • Vertical bar • To make conversions easier, we can set off each factor by a vertical bar • Convert 5 dm3 to cm3

  32. Factor Label Method • In the factor label method, units are treated as factors, and as such, can be divided out • Example on board

  33. Density • Density is mass per unit of volume • Density = mass/volume • D=m/v • Unit is g/ml

  34. Assignment • Complete • Exercises 13-24 on pages 30-31 • Exercises 29, 32, 38, and 39 on page 32 of the text • Exercises 44, 45,46 on page 35 of your text • Worth 20 points • Due: Monday

  35. Chapter Review • Complete • chapter review questions • 48 all, 49a, 50 all, 51 all, 54, 55, 57, 59, 60, 61, 62, 64, 65, 66 all, 68 all, 69 all, 70, 71 all, 73 all, 83, 85, 86, 94, and 95 on pages 36-38 of your text • Remember, these questions will be very similar to those found on the unit test, so do them all • This will be collected for a possible 25 points

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