Theory and Law Exercise \(\PageIndex{1}\) Tell whether each statement is most similar to a hypothesis, observation, theory, or law. This box of cereal is less expensive than that one. Answer observation The larger the box of cereal, the lower the price per ounce is. Answer law If I buy the largest package of food I can eat before it goes stale, I will save money on groceries. Answer hypothesis The cost associated with packaging plays an important role in setting the price of groceries. For the size of the packaging, the cost does not increase proportionally to the volume. Therefore, the fraction of the price that is going towards packaging is smaller for larger sizes. Answer theory Extensive and Intensive Properties Exercise \(\PageIndex{1}\) Tell whether each is an extensive or intensive property. (a) length (b) mass (c) temperature (d) the weight of a piece of clay (e) the color of the clay (f) the price of a bunch of apples (g) the price per pound of the apples Answer (a) Extensive Answer (b) Extensive Answer (c) Intensive Answer (d) Extensive Answer (e) Intensive Answer (f) Extensive Answer (g) Intensive Exact and Measured Numbers Exercise \(\PageIndex{1}\) Tell whether each number represents an exact number or an uncertain, measured number. I have 12 coins. Answer Exact The total mass of my coins is 27.420 g. Answer Uncertain (measured) The average mass of each coin is therefore 2.2850 g per coin. Answer Uncertain (measured) One of the metals used to make the coins is nickel, which has a density of 8.908 g/cm 3 . Answer Uncertain (measured) The prefix "kilo" means 1000, so there are 1000 g in a kg. Answer Exact That means the total mass of my coins is 0.027420 kg. Answer Uncertain (measured) Precision and Accuracy Exercise \(\PageIndex{1}\) You used a calibration mass to test three balances. The mass is 25.000 g. Your results are below. 0 1 2 3 NaN Balance A Balance B Balance C Trial 1 24.81 g 24.97 g 24.57 g Trial 2 24.69 g 25.28 g 24.69 g Trial 3 24.93 g 24.93 g 24.63 g Trial 4 25.09 g 25.06 g 24.66 g Trial 5 25.33 g 25.11 g 24.55 g Average 24.97 g 25.07 g 24.62 g Standard Deviation 0.25 g 0.14 g 0.06 g Which balance is the most precise? Answer Balance C. (It has the lowest standard deviation. The trials are closest together.) Which balance is the least precise? Answer Balance A. Which balance is the most accurate? Answer Balance A. (The average value is closest to 25.000 g) Which balance is the least accurate? Answer Balance C. What is the percent error of balance B? (Use the average measurement to calculate.) Answer 0.3 %.