Chapter Two Q & A

Metric Prefix Abbreviation Meaning Centi- c 10 − 2 Kilo- k 10 3 Mega- M 10 6 Pico- p 10 − 12 Deci- d 10 − 1 Metric Prefix Abbreviation Meaning Milli- m 10 − 3 Giga- G 10 9 Nano- n 10 − 9 Mega- M 10 6 Micro- u 10 − 6 Unit What’s Measured Abbreviation Microliter volume u L Kilogram mass kg Megameter length Mm Nanogram mass ng Milliliter volume ml Unit What’s Measured Abbreviation Gigagram mass Gg Centimeter length cm Deciliter volume dL Picometer length pm Kilogram mass kg Arrange each of the following from smallest to largest: a. Microliter < milliliter < gigalitre b. Centigram < decigram <megagram c. Picometer <micrometer < kilometer d. Nanoliter <milliliter < centiliter Which of the two given units is the more logical unit for expressing each of the following measurements? a. Length of an ant’s body (centimeter or micrometer ) b. Width of a football field ( meter or kilometer) c. Volume of glass of milk (megaliter or milliliter ) d. Mass of an elephant (gram or kilogram ) A person is told that there are 27 people in attendance at a meeting and also that the speed of a bicyclist is 27 miles per hour. What is the difference relative to uncertainty between the value of 27 in these two pieces of information? 27 people is a certain number but 27 miles per hour has potential for uncertainty. The fact that there are 27 people in attendance is absolutely and fully exact - no uncertainty there. On the other hand, speed (velocity) is measured, which means it can vary/not be precise which is why uncertainty is present in that piece of information. Indicate whether the number in each of the following statements is exact or an inexact number: a. A classroom contains 63 students: exact b. The car is traveling at a speed of 56 miles per hour: inexact

c. The temperature on the back porch is -3°F: inexact d. There are 3 feet in a yard: exact Indicate whether each of the following quantities would involve an exact number or an inexact number: a. The number of pages in a chemistry textbook: exact b. The number of teeth in a bears mouth: exact c. The distance from Earth to the sun: inexact d. The temperature of a heated oven: inexact Identify the estimated digit in each of the following measurements: a. 317: 7 b. 317.0: 0 c. 3.170: 0 d. 0.0317: 7 What is the magnitude of the uncertainty (+-10, +-0.01, etc.) associated with each of the Following measurements: (a) 317 has the uncertainty of +/- 10 (b) 317.0 has the uncertainty of +/- 0.1 (c) 3.170 has the uncertainty of +/- 0.001 (d) 0.0317 has the uncertainty of +/- 0.0001 Indicate to what decimal position readings should be recorded (nearest 0.1, 0.01, etc.) for measurements made with the following devices: a. A ruler with a smallest scale marking of 1 cm (nearest 0.1cm, one decimal place) b. A device for measuring angles with a smallest scale marking of 1° (nearest 0. 1°, one decimal place) c. A thermometer with a smallest scale marking of 0.1°F (nearest 0.1° F, two decimal places) d. A graduated cylinder with a smallest scale marking of 10 mL (nearest 1 mL, no decimal places) Determine the number of significant figures in each of the following measured values: a. 0.372: 3 b. 0.0372: 3 c. 0.37202: 5 d. 0.37200: 5 Determine the number of significant figures in each of the following measured values: a. 303.00: 5 b. 30,300: 3 c. 5,703,000: 4 d. 570,002: 6 In which of the following pairs of numbers do both members of the pair contain the same number of significant figures: a. 345,000 and 340,500: different b. 2302 and 2320: different c. 0.6600 and 0.66: different d. 936 and 936,000: same Complete the following table by filling in the blanks in each row with numerical values that are consistent with the number given in the first column. The first row is completed as an example Measured number, number of sig figs, estimated digit in measurement Example: 3.25, 3, the 5, +-0.01 a. 0.030, 2, the 0, +-0.001 b. 2100, 2, the 1, +-100 c. 7005, 4, the 5, +-1 d. 1.23, 3, the 3, +-0.01

For each of the following numbers, will the exponent be positive, negative, or zero when the number is expressed in scientific notation a. 50.031 5.0031× 10 1 (Exp: Positive) one decimal place to the left 5 Sig Figs b. 650,010 6.5001× 10 5 (Exp: Positive) five decimal places to the left 5 Sig Figs c. 0.1030 1.030× 10 − 1 (Exp: Negative) one decimal place to the right 4 Sig Figs d. 735 7.35× 10 2 (Exp: Positive) two decimal places to the left 3 Sig Figs Express the following measured values in scientific notation to the correct number of significant figures: a. 37.22 3.722 × 101 b. 0.00102 1.02 × 10−3 c. 34.000 3.4000 × 101 d. 234,000 2.34 × 105 Change each of the following measured values from scientific notation to decimal notation: a. 3.721 × 103 in decimal notation is 3721. b. 3.7210 × 102 in decimal notation is 372.10 c. 6.76 × 10-2 in decimal notation is 0.0676 d. 6.7600 × 10-2 in decimal notation is 0.067600 Carry out the following multiplications and divisions, expressing your answer in scientific notation to the correct number of significant figures: (ALL 4 have TWO SIG FIGS ***) a. (4.0 x 10 4 ) x (1.32 x 10 8 ) = 5.28 (calc ans) rounded = 5.3 b. (3.200 x 10 7 ) x (1.10 x 10 − 2 ) x (2.3 x 10 7 ) =8.096 (calc) rounded = 8.1 c. 6.0 x 10 − 5 3. 0 x 10 3 d. (3.2 x 10 4 ) x 10 2 ) x (3.31 x 10 6 ) 4.00 x 10 − 3 ) x (2.0 x 10 6 ) What is the uncertainty, in terms of a power of 10, associated with each of the following measured values? a. 4.30 x 10 − 2 ( 10 − 2 x 10 − 2 ) = 10 − 4 b. 4.300 x 10 − 1 ( 10 − 3 x 10 − 1 ) = 10 − 4 c. 4. 3 x 10 3 ( 10 − 1 x 10 3 ) = 10 − 2 d. 4.300 x 10 5 ( 10 − 3 x 10 − 5 ) = 10 − 2 Write each of the following numbers in scientific notation to the number of significant figures indicated in parentheses. a. 0.303030 (four) 3.030×10−1 b. 15.0670 (three) 1.51×101 c. 3,263,300 (three) 3.26×106 d. 32,000,0071 (four) 3.200×107 Give the two forms of the conversion factor that relate each of the following pairs of units: a. Days and hours 24 hours 1 Day or 1 Day 24 hours

b. Decades and centuries 10 years 1 Decade or 1 Decade 10 years c. Feet and yards 3 feet 1 yard or 1 yard 3 feet d. Quarts and gallons 4 quarts 1 gallon or 1 gallon 4 quarts Give the two forms of the conversion factor that relate each of the following pairs of units: a. ng and g 1ng=1× 10 − 9 g (over 1ng, or 1ng written over equation) b. dL and L 1dL=0.1L (1dL/0.1L or 0.1L/1dL c. m and Mm 1m=1× 10 − 6 Mm (1m/1× 10 − 6 Mm or 1× 10 − 6 Mm/1m) d. psec and sec 1psec=1× 10 − 12 sec (1psec/1× 10 − 12 sec or 1× 10 − 12 sec/1psec) Indicate whether the following are EXACT or INEXACT conversions relative to Sig Figs: a. 1 gallon = 16 cups (inexact, conversion from liters may vary) b. 1 week = 7 days (exact, there are exactly 7 days in a week) c. 1 pint = 0.4732 liter (exact, four significant figures) d. 1 mile = 5280 feet (exact) ***Using dimensional analysis, convert each of the following measurements to meters: a. 2.7 x 10 3 mm ( Conversion factor: 1mm = 0.001m) 2.7 × 10 3 mm × 0.001 m/1mm = 2.7m b. 24 µm ( Conversion factor: 1 µm = 1 x 10 − 6 m) 24 µm × 1 × 10 − 6 m/1 µm = 2.4 × 10 − 5 m c. 0.003 pm ( Conversion factor: 1pm = 1.0 x 10 − 12 m) 0.003pm × 1.0 x 10 − 12 m/1pm = 3.0 x 10 − 15 m d. 4.0 x 10 5 cm ( Conversion factor: 1cm = 0.01m) 4 .0 × 10 5 cm × 1m/ 10 2 c m = 4.0 × 10 3 m ***A typical loss of water through sweating for a human is 450 mL per day. What is the volume, in liters, of sweat produced per day? (To convert from 450 mL to L, we need the equivalence statement 10 3 mL is equal to 1L.) Therefore, water lost through sweating per day. *** The smallest bone in the human body, which is in the ear, has a mass of 0.0030g. What is the mass of this bone in pounds? (To convert from g to lb, remember 1.00 lb = 454 g) The conversion is carried out as follows:

c. 0.400040 lb 4 Sig Figs d. 423,000 lb 4 Sig Figs ***A sample of sand is found to have a mass of 12.0 g and to have a volume of 2.69 cm 3 . What is its density in grams per cubic centimeter? (Formula for density, and densities of solid, liquid, and gas:) * * * * = 4.6 g/ cm 3 *** Silver metal has a density of 10.40 g/ cm 3 . What is the volume, in cubic centimeters, of a 100.0-g bar of silver metal? (Calculate as above with formula for density, solid, liquid, gas.) = 9.615 cm 3 *** Nickel metal has a density of 8.90 g/ cm 3 . How much does 15 cm 3 of nickel metal weigh in grams? * = 134 g *** Air has a density of 1.29 g/L at room temperature. State whether each will rise or sink: a. Helium gas (density = 0.18 g/L) FLOAT (density smaller than air) b. Argon gas (density = 1.78 g/L) SINK (density larger than air) (Density of object > density of air = object sinks, density of object < density of air = object floats, densities of object & air are very close = object may assume intermediate state. *** A two-gram sample of a red-colored liquid is found to have a volume of four cubic centimeters. Calculate the liquid’s density using the following uncertainty specifications, and express your answers in scientifica notation . (Density = mass (m) / Volume (V) a. 2.00 g and 4.000 cm 3 (3 sig figs) = 0.500 g/ cm 3

b. 2.000 g and 4.0 cm 3 (2 Sig figs) = 0.50 g/ cm 3 c. 2.0000 g and 4.000 cm 3 (4 Sig figs) = 0.5000 g/ cm 3 d. 2.000 g and 4.0000 cm 3 (4 Sig figs) = 0.5000 g/ cm 3 *** Calculate the volume, in milliliters, for each of the following 66.0-g masses of substances. a. 66.0 g of blood plasma (density = 1.027 g/mL) =64.3 mL b. 66.0 g of dry air (density = 1.29 g/L) * convert* =51,200 mL c. 66.0 g of lead metal (density = 11.3 g/ cm 3 ** = 5.84 mL d. 66.0 g of milk (density = 1.03 g/mL) = 64.1 mL *** A Comfortable temperature for bathtub water is 95°F. What temperature is this is degrees Celsius? = 35 °C *** The body temperature for a hypothermia victim is found to have dropped to 29.1°C. What is this temperature in degrees Fahrenheit?