Chapter 2: Scientific Measurement

1. Chapter 2: Scientific Measurement

2. Measurements & Their Uncertainty • Scientific Notation • Using scientific notation makes it easier to write very large or very small numbers • In scientific notation the first number is between 1 and 10 (less than 10) and it is multiplied by 10 to some power • The exponent tells you how many places to move the decimal point • If the exponent is positive then the number in decimal notation is > 10 • If the exponent is negative then the number in decimal notation is < 1

3. Examples

4. Accuracy and Precision • Accuracy: how close a measurement comes to the true and accepted value • Precision: how close a series of measurements are to each other • Percent error: used to assess the accuracy of the data

5. Significant Figures in Measurements • When you make a measurement you should report all of the digits that are known and the last that is an estimate • Both the certain digits and the uncertain digit are considered significant figures unless some of the digits are just being used as placeholders

6. Rules for determining the # of sig figs in a measurement… • All nonzero digits are significant • All conversion factors and counting numbers have infinite sig figs • Leading zeroes never count • Embedded zeroes always count • Trailing zeroes only count if there is a decimal point in the number

7. Examples • 0.0028 kg • 3.00 m • 0.0250 L • 40 g • 40. g • 40.0 g • 9003 cm

8. Significant Figures in Calculations • When adding or subtracting…round your answer so that it has the same # of digits to the right of the decimal point as the measurement with the fewest digits to the right of the decimal point • Ex: 200.005 g + 10.2 g + 7000. g • Ex: 14.2 g + 8.73 g + 0.912 g

9. When multiplying or dividing…round your answer so that it has the same # of sig figs as the measurement with the fewest sig figs • Ex: 7.55 m x 0.3400 m • Ex: 8.3 g ÷ 2.22 mL

10. The International System of Units (SI) • SI Base Units

11. Prefixes used with SI units • Prefixes greater than 1

12. Prefixes less than 1

13. Converting between SI units • Moving the decimal point • Examples • How many hm is 380 m? • How many kilometers is 17.0 decimeters? • Convert 2944 mg to dag

14. Units of Volume • Volume: the space occupied by any sample of matter • Volume is not a base quantity, it is a derived quantity • Formula for volume is V = l • w • h • Since the base unit of length is m, the base unit of volume is m3 • Commonly used units are mL and L (not SI)

15. Glassware used to measure volume of a liquid • Graduated cylinder • Pipet • Buret • Volumetric flask

16. Units of Temperature • Temperature: a measure of the hotness or coldness of an object (based on the kinetic energy of its particles) • Temperature scales • Celsius—water freezes at 0°C, boils at 100°C • Kelvin—water freezes at 273 K and boils at 373 K • K = °C + 273

17. Examples • A recipe calls for a cake to be baked at 350°F, which is 177°C. What is this temperature in Kelvin? • Oxygen has a boiling point of 90.0 K. What is this temperature in Celsius? • Absolute zero: 0 K, the lowest temperature that can ever exist

18. Units of Energy • Energy: the ability to do work or transfer heat • SI unit of energy is the joule (J) • Relationship between joules and calories: 1 calorie = 4.184 joules • Calories on food packages are actually kilocalories so 1 food Calorie = 1000 calories

19. Conversion Problems • Conversion factor: a ratio of 2 equivalent measurements that are expressed in different units • For the equality 1 day = 24 hours there are 2 conversion factors: • Example: Write 2 conversion factors for the equality 16 ounces = 1 pound • Conversion factors have infinite sig figs

20. The larger number always gets the smaller unit and vice versa • When solving problems with conversion factors, the unit that you start with always goes on the bottom; the unit that you end with goes on the top

21. Dimensional analysis: a problem-solving technique that uses conversion factors • Steps for completing dimensional analysis problems • Start with the number given in the problem • Multiply by the appropriate conversion factor • Round your answer to the proper sig figs • Give your answer a unit

23. One step problems • Convert 6.5 days into hours. • How many tablespoons is 14 teaspoons? • How many weeks is 43 days?

24. Multi-step problems • Convert 3.9 hours into seconds. • How many minutes are in 5.0 days? • There are 12 inches in a foot and 3 feet in a yard. How many yards is 57 inches?

25. Measuring Density • Density: • The density of a particular substance at a given temp is always the same, regardless of the sample size • Solids and liquids are usually measured in g/cm3 (or g/mL) while gases are usually in g/L • Usually as temp increases a substance’s density decreases

26. Density Calculations • A piece of metal has a volume of 245 mL and a mass of 612 g. What is the density of the metal? • The density of a substance is 1.63 g/mL. What is the mass of 250 mL of the substance?

27. A bar of gold has a mass of 13.0 g. What is its volume?