3.1 MEASUREMENTS AND THEIR UNCERTAINTY Section Review Objectives Convert measurements to scientific notation Distinguish among the accuracy, precision, and error of a measurement Identify the number of significant figures in a measurement and in the result of a calculation Vocabulary measurement scientific notation accuracy precision accepted value experimental value error percent error significant figures Key Equations Error = experimental value accepted value error Percent error = 100% acce pted value Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. The 1 of a measurement describes how close the 1. measurement comes to the true value. The 2 of a measure- 2. ment depends on its reproducibility. An 3 is a value 3. measured in the lab. 4 is calculated by subtracting the 4. 5 from an experimental value. Percent error is calculated 5. by dividing the 6 of the error by the accepted value and 6. then multiplying by 7. 7. Large and small numbers are more easily handled when 8. expressed in 8. Significant figures in a measurement include 9. all of the digits that are 9 plus a last digit that is 10. 10. Chapter 3 Scientific Measurement 55
Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 11. Scientific notation is used to express large numbers in convenient form. 12. Significant figures include all the digits that can be known accurately plus a last digit that must be estimated. 13. An answer to calculations done with scientific measurements cannot be more precise than the least precise measurement. Part C Matching Match each description in Column B to the correct term in Column A. Column A Column B 14. accuracy 15. measurement 16. precision 17. scientific notation 18. experimental value a. measure of how close a series of measurements are to one another b. measure of how close a measurement comes to the actual value c. digits in a measurement that are known plus one that is estimated d. a value determined in the laboratory e. a quantity that has both a number and a unit 19. significant figures Part D Questions and Problems Answer the following questions or solve the following problems in the space provided. Show your work. 20. Give the number of significant figures in the following measurements. a. 3.85 10 3 dm a. b. 17.30 cm 3 b. c. 0.0037 mm c. 21. Perform the following operations and give the answers in standard exponential form with the correct number of significant figures. a. 37.2 ml 18.0 ml 380 ml b. 0.57 cm 0.86 cm 17.1 cm f. a method of expressing numbers as a product of a coefficient and a power of 10. c. (8.13 10 4 ) (3.8 10 2 ) 56 Core Teaching Resources
3.2 THE INTERNATIONAL SYSTEM OF UNITS Section Review Objectives List SI units of measurement and common SI prefixes Distinguish between the mass and weight of an object Convert between Celsius and Kelvin temperature scales Vocabulary International System of Units (SI) meter (m) liter (L) weight kilogram (kg) gram (g) temperature Celsius scale Kelvin scale absolute zero energy joule (J) calorie (cal) Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. The International System of Units (SI) is a revision of the 1. 1 system. There are 2 SI base units. In SI, the base 2. unit of length is the 3. 3. The space taken up by a cube that is 10 cm on each edge is 4. one 4. A measure of the pull of gravity on an object of 5. given mass is its 5. The mass of one cubic centimeter of 6. water at 4 C is one 6. Scientists commonly use two 7. equivalent units of temperature, the degree 7 and the 8. 8. The 9 and the 10 are common units of energy. 9. 10. Chapter 3 Scientific Measurement 57
Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 11. The SI base unit of mass is the milliliter. 12. A decigram is 100 times smaller than a gram. 13. The SI unit of volume is derived from the unit of length. 14. There are six basic SI units of measurement. Part C Matching Match each description in Column B to the correct term in Column A. Column A Column B 15. Kelvin scale 16. International System of Units (SI) 17. temperature 18. meter 19. calorie 20. Celsius scale 21. liter 22. joule 23. weight 24. absolute zero 25. kilogram 26. gram 27. energy a. quantity of heat that raises the temperature of 1 g of pure water by 1 C. b. the capacity to do work or to produce heat c. the SI unit of energy d. non-si unit of volume e. standardized system of measurement based on the metric system f. mass unit commonly used in chemistry g. the SI unit of length h. force that measures the pull of gravity on a given mass i. zero point on the Kelvin scale equal to 273.15 C j. SI base unit of mass k. temperature scale on which the freezing point of water is 273.15 and its boiling point is 373.15 l. freezing scale that sets the freezing point of water at 0 and its boiling point at 100 m. measure of how hot or cold an object is 58 Core Teaching Resources
Part D Questions and Problems Answer the following in the space provided. 28. What is the volume of a board that measures 1.8 cm by 8.8 cm by 30.5 cm? 29. Hydrogen boils at 20K. What is the boiling point of hydrogen on the Celsius scale? 30. What is the symbol and meaning of each prefix? a. pico- a. b. kilo- b. c. micro- c. d. centi- d. Chapter 3 Scientific Measurement 59
3.3 CONVERSION PROBLEMS Section Review Objectives Construct conversion factors from equivalent measurements Apply the techniques of dimensional analysis to a variety of conversion problems Solve problems by breaking the solution into steps Convert complex units, using dimensional analysis Vocabulary conversion factor dimensional analysis Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. Whenever two measurements are equal, or equivalent, 1. a ratio of these two measurements will equal 1. 2. A ratio of equivalent measurements is called a 2. When 3. a measurement is multiplied by a conversion factor, the value 4. of the measurement 3. 5. In 4, the units that are a part of the measurements 6. are used to help solve the problem. The form of the conversion 7. factor that is used is the one in which the unit of the 5 is 8. in the denominator. 9. Many complex word problems can be solved by breaking the 10. solution into 6. When converting between units, it is often necessary to use more than one 7. In doing multistep problems, it is important to check that the numerator and 8 of each conversion factor are equivalent. When the 9 cancel, you should be left with the unit of the 10. 60 Core Teaching Resources
Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 11. The units of a conversion factor must cancel. 12. The conversion factor for changing between grams and milligrams is 1 g. 100 0 mg 13. Multiple conversion factors can be used to solve complex conversion problems. 14. If density mass/volume, then mass density/volume. 15. When two measurements are equal, a ratio of these two measurements will equal unity. Part C Questions and Problems Answer the following in the space provided. 16. Make the following conversions using Tables 3.1 and 3.2. Write your answers in scientific notation. a. 125 g to kilograms b. 0.12 L to ml 17. If 1500 white blood cells are lined up side by side, they would form a row 1.0 inch long. What is the average diameter in micrometers of a single white blood cell? (1 inch 2.54 cm) 18. A radio wave travels 186,000 miles per second. How many kilometers will the wave travel in one microsecond? (1 mile 1.61 km) Chapter 3 Scientific Measurement 61
3.4 DENSITY Section Review Objectives Calculate the density of a material from experimental data Describe how density varies with temperature Key Term density Key Equation mass Density = vo lume Part A Completion Use this completion exercise to check your understanding of the concepts and terms that are introduced in this section. Each blank can be completed with a term, short phrase, or number. The ratio of the mass of an object to its volume is its 1. 1. Density is an 2 property that depends only on the 3 2. of a substance, not on the size of the sample. 3. Part B True-False Classify each of these statements as always true, AT; sometimes true, ST; or never true, NT. 4. The density of a substance decreases as its temperature is increased. 5. Density has units of grams per cubic centimeter. 62 Core Teaching Resources
Part D Questions and Problems Solve the following problems in the space provided. Show your work. 6. A rock has a mass of 127 g and displaces 32.1 ml of water. What is the density of the rock? 7. A 1.00-L sample of carbon tetrachloride has a mass of 1.58 kg. What is the density of this substance in g/cm 3? Chapter 3 Scientific Measurement 63