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Scientific Notation, Metric System, & Unit Conversion Review ..., Slides of Physics

Polytechnic University of the Philippines (PUP)Physics

Scientific Notation, Metric System, & Unit Conversion. Review Worksheet. Scientific Notation. 1. Rewrite the following numbers in scientific notation, ...

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Physics 151
Scientific Notation, Metric System, & Unit Conversion
Review Worksheet
Scientific Notation
1. Rewrite the following numbers in scientific notation, in simplest form. Include units. Use appropriate
significant figures!
a. Altitude of summit of Mt. Ka‘ala (highest point on O‘ahu): 4020 ft =
b. Altitude of summit of Mauna Kea: 13,796 ft =
c. Thickness of a human hair: 0.015 cm =
d. Wavelength of reddish light: 0.0000007 m =
e. Height of your instructor: 1.80 m =
f. Number of galaxies in the universe: 1 trillion galaxies =
g. Age of the universe in seconds: 430,000,000,000,000,000 s =
h. Volume of a hydrogen atom: 0.000 000 000 000 000 000 000 000 621 cm3 =
2. Calculate the following, and write your answer to each in scientific notation. Try to do (a)–(i) first wi thout the
aid of your calculator, then check your answers by redoing them with your calculator. Assume that parts (a)–(h)
contain exact numbers with infinite precision; for parts (i)–(n), express only the appropriate number of significant
figures in your final answer. [Note that (b), (c), (g), (l), and (m) contain division signs, not plus signs.]
a. 1010 × 104 =
b. 1010 ÷ 104 =
c. 1010 ÷ 10–4 =
d. 1010 + 104 =
e. 1010 − 104 =
f. (2 × 105) × (3 × 1012) =
g. (3.5 × 1017) ÷ (7 × 108) =
h. 107 − (3 × 106) =
i. (42.3 × 10–5) + (5.77 × 10–4) =
j. (34.9 × 106) × (212 × 10–15) =
k. (0.88 × 10–3) × (6.3 × 10–10) =
l. (9.876 × 1035) ÷ (5.4321 × 10–13) =
m. mass of Earth ÷ mass of Moon = (5.974 × 1027 g) ÷ (7.348 × 1025 g) =
n. mass of Earth − mass of Moon = (5.974 × 1027 g) − (7.348 × 1025 g) =
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Physics 151

Scientific Notation, Metric System, & Unit Conversion

Review Worksheet

Scientific Notation 1. Rewrite the following numbers in scientific notation , in simplest form. Include units. Use appropriate significant figures! a. Altitude of summit of Mt. Ka‘ala (highest point on O‘ahu): 4020 ft = b. Altitude of summit of Mauna Kea: 13,796 ft = c. Thickness of a human hair: 0.015 cm = d. Wavelength of reddish light: 0.0000007 m = e. Height of your instructor: 1.80 m = f. Number of galaxies in the universe: 1 trillion galaxies = g. Age of the universe in seconds: 430,000,000,000,000,000 s = h. Volume of a hydrogen atom: 0.000 000 000 000 000 000 000 000 621 cm^3 = 2. Calculate the following, and write your answer to each in scientific notation. Try to do (a)–(i) first without the aid of your calculator, then check your answers by redoing them with your calculator. Assume that parts (a)–(h) contain exact numbers with infinite precision; for parts (i)–(n), express only the appropriate number of significant figures in your final answer. [Note that (b), (c), (g), (l), and (m) contain division signs, not plus signs.] a. 1010 × 104 = b. 1010 ÷ 104 = c. 1010 ÷ 10 –^4 = d. 1010 + 104 = e. 1010 − 104 = f. ( 2 × 105 ) × (3 × 1012 ) = g. (3.5 × 1017 ) ÷ (7 × 108 ) = h. 107 − (3 × 106 ) = i. (42.3 × 10 –^5 ) + (5.77 × 10 –^4 ) = j. (34.9 × 106 ) × (212 × 10 –^15 ) = k. (0.88 × 10 –^3 ) × (6.3 × 10 –^10 ) = l. (9.876 × 1035 ) ÷ (5.4321 × 10 –^13 ) = m. mass of Earth ÷ mass of Moon = (5.974 × 1027 g) ÷ (7.348 × 1025 g) = n. mass of Earth − mass of Moon = (5.974 × 1027 g) − (7.348 × 1025 g) =

Powers of Ten 3. Insert the correct metric prefix abbreviations (be careful to distinguish upper case from lower case!): 10 –^2 m = 1 _____m 109 y = 1 _____y 103 W = 1 _____W 10 –^3 m = 1 _____m 106 W = 1 _____W 10 –^6 s = 1 _____s 10 –^9 m = 1 _____m 103 g = 1 _____g 109 bytes = 1 _____B 106 Hz = 1 _____Hz 10 –^12 s = 1 _____s 1012 bytes = 1 _____B ( units: m = meter; g = gram; s = second; Hz = hertz, a unit of frequency; y = year; W = watt, a unit of power; B = byte, a unit of computer information) 4. Match each of the following length units to the distance that it is best or most frequently used to describe: A. Size of an ant _____ 0.1 nm = 1 Å B. Size of a person _____ 100 nm = 1000 Å C. Distances between neighboring stars _____ 100 μm D. Diameter of human hair _____ 1 mm E. Size of an atom _____ 100 cm = 1 m F. Size of viruses and small bacteria _____ 1 km G. Distances within our Solar System _____ 10^8 km H. Distances around Oahu _____ 10^13 km Significant Figures 5. How many significant figures are represented in each of the following numbers? a. 579.420 b. 3. c. 2 × 1011 d. 50. e. 3800 f. 5.60 × 1048 g. 243. h. 9.0000 × 10 –^9 i. 0.00000030 j. 8 Unit Conversions 6. a. Starting with your age in years, calculate your age in days. (You do not need to be exact: forget about leap days, etc.) b. Approximately how many days long is your total life expectancy? 7. Use your weight in pounds (while standing on the surface of the Earth) to calculate your mass in kilograms and in grams. (1 kg weighs approx. 2.205 lb on the surface of the Earth) This is a useful thing to know, since almost every other country in the world uses kilograms!

Scientific Hypotheses 9. Is each of the following statements a testable scientific hypothesis , or not? a. Light travels slower in glass than in air. b. Love is more important than knowledge. c. All objects fall 4.9 meters during the first second after release in a vacuum. d. The universe is filled with tiny particles called hypotons, which have no mass, no charge, and no known form of interaction with ordinary matter. e. Vanilla tastes better than chocolate. f. The majority of Americans prefer vanilla to chocolate. g. All human actions and choices are predestined. 10. Imagine that you are living long ago, and you are having a discussion about the shape of the world with your colleagues. Devise a simple test or experiment that you could perform to test (either support or disprove) one of the following hypotheses: a 1. The surface of the Earth is an infinite flat plane, or a 2. The surface of the Earth is (nearly) spherical. For a bigger challenge: similarly devise a test for each of the following two scientific hypotheses. ( Thought question: How do we even know today , with modern technology, that they are true?) b. The Earth spins. c. The Earth orbits the Sun, and not the other way around.

Scientific Notation, Metric System, & Unit Conversion Review Worksheet

SOLUTIONS

1. a. 4.02 × 103 ft (or 4.020; it is unclear whether the final zero is significant) b. 1.3796 × 104 ft c. 1.5 × 10 –^2 cm d. 7 × 10 –^7 m e. 1.80 m (this is the same as writing 1.80 × 100 m) f. 1 × 1012 galaxies (or simply: 10^12 galaxies) g. 4.3 × 1017 s (or 4.30, or 4.300, etc., although there are probably only 2 sig. figs) h. 6.21 × 10 –^25 cm^3 2. Assume the values in parts (a)–(h) are exact numbers with infinite precision: a. 1010 × 104 = 10(10 + 4)^ = 10^14 b. 1010 ÷ 104 = 10(10^ –^ 4)^ = 10^6 c. 1010 ÷ 10 –^4 = 10(10^ –^ – 4)^ = 10^14 d. 1010 + 104 = 1.000001 × 1010 e. 1010 − 104 = 9.99999 × 109 f. (2 × 105 ) × (3 × 1012 ) = (2 × 3) × (10^5 × 1012 ) = 6 × 10 (5 + 12)^ = 6 × 1017 g. (3.5 × 1017 ) ÷ (7 × 108 ) = (3.5 ÷ 7) × (10^17 ÷ 108 ) = 0.5 × 10 (17^ –^ 8)^ = 0.5 × 109 = 5 × 108 h. 107 − (3 × 106 ) = (10 × 106 ) – (3 × 106 ) = (10 – 3) × 106 = 7 × 106 For parts (i)–(n), observe significant figures : i. (42.3 × 10 –^5 ) + (5.77 × 10 –^4 ) = 1.000 × 10 –^3 j. (34.9 × 106 ) × (212 × 10 –^15 ) = 7.40 × 10 –^6 k. (0.88 × 10 –^3 ) × (6.3 × 10 –^10 ) = 5.5 × 10 –^13 l. (9.876 × 1035 ) ÷ (5.4321 × 10 –^13 ) = 1.818 × 1048 m. (5.974 × 1027 g) ÷ (7.348 × 1025 g) = ratio of mass of Earth to mass of Moon = 81.30 (or: 8.130 × 101 ) n. (5.974 × 1027 g) − (7.348 × 1025 g) = difference of mass of Earth and mass of Moon = 5.901 × 1027 g 3. 10 –^2 m = 1 cm (centimeter) 109 y = 1 Gy (gigayear) 103 W = 1 kW (kilowatt) 10 –^3 m = 1 mm (millimeter) 106 W = 1 MW (megawatt) 10 –^6 s = 1 μs (microsecond) 10 –^9 m = 1 nm (nanometer) 103 g = 1 kg (kilogram) 109 bytes = 1 GB (gigabyte) 106 Hz = 1 MHz (megahertz) 10 –^12 s = 1 ps (picosecond) 1012 bytes = 1 TB (terabyte) 4. A. Size of an ant _E 0.1 nm = 1 Å B. Size of a person _F 100 nm = 1000 Å C. Distances between neighboring stars _D 100 μm D. Diameter of human hair _A 1 mm E. Size of an atom _B 100 cm = 1 m F. Size of viruses and small bacteria _H 1 km G. Distances within our Solar System _G 10^8 km H. Distances around Oahu _C 10^13 km 5. a. 6 b. 9 c. 1 d. 2 e. 2 (or 3 or 4… it’s ambiguous!) f. 3 g. 3 h. 5 i. 2 j. 1

6. a. Assuming an age of 20. years: (20. y) × (365 d / 1 y) = 7300 d b. Assuming an 80.-year life expectancy: (80. y) × (365 d / 1 y) = 29,000 d (rounded to 2 significant figures) 7. Assuming a weight of 150. pounds: (150. lb) × (1 kg / 2.205 lb) = 68.0 kg