Chapter 5 Measurements and Calculations Section 5.1 Scientific Notation and Units Key Terms Measurement Scientific notation Units English system Metric system International System (SI) Volume Liter Milliliter Mass Gram Questions 1. When writing numbers using scientific notation, numbers greater than one have _____ exponents and numbers less than one have _____ exponents. 2. Change the following to scientific notation: a. 8,475,000 b. 0.0000754 c. 1,000 d. 0.35724 3. Copy and complete the table below. English unit Metric unit Length meter Volume quart Mass pound 4. How many millimeters are in 50 cm? 5. Which is larger, a liter or a quart? Section 5.2 Uncertainty in Measurement and Significant Figures Key Terms Significant figures Rounding off Questions 1. Why are all measurements uncertain? 2. What are the three types of zeros in a number? Which type is always significant? Which type is never significant? Which type is sometimes significant? 3. Copy the following numbers, and mark each significant zero with an arrow. a. 0.003042 b. 1.4030 c. 1000 d. 0.060 e. 50.0 f. 10.47020 g. 250. 4. How many significant figures are in each number below? a. 0.003042 b. 1.4030 c. 1000 d. 0.060 e. 50.0 f. 10.47020 g. 250. 5. Without doing the calculation, tell how many significant figures should be in each result. a. 3.2 + 4.17 + 12.43 b. 1.3478 – 0.02 c. 4.6 x 3.435 d. (4.2 x 10-5) x 3.74 ÷ 6.783 e. 50 – 0.00473 6. Perform the calculations, and determine the results from question 5. 7. State the number of significant figures in a measurement made with each ruler: a. b. c. Section 5.3 Problem Solving and Unit Conversions Key Terms Conversion factor Equivalence statement Dimensional analysis Fahrenheit scale Celsius scale Kelvin scale (absolute) Density Specific gravity Questions 1. What is an equivalence statement? How many conversion factors can be created from one equivalence statement? Choose an equivalence statement from Table 5.7, and write all the possible conversion factors from it. 2. Write a conversion factor or factors for these problems. Do not do the calculation. a. 37 cm x _____ = ? in. b. 4.2 qt x _____ = ? L c. 2.2 kg x _____ = ? pounds d. 3.5 mi x _____ = ? m 3. Complete the conversions for each of the problems in question 2. 4. You run a 100-yd dash in 9.8 seconds. What is your speed in miles per hour? 5. Convert the following temperatures. a. 30. °C to °F b. 72 °F to K c. 14 K to °C d. 342 K to °F 6. A certain liquid has a density of 0.79 g/mL. What volume of this liquid has a mass of 15.0 g? 7. For each of the following, decide which block is more dense: the block on the left or the block on the right, or state that it cannot be determined. Explain your answers. a. b. c. d.