PART 4: The other thing we need to practice for this class is how to work with b
ID: 1999898 • Letter: P
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PART 4: The other thing we need to practice for this class is how to work with big numbers and how to deal with the fact that there are so many different words for units. Let’s start with examples of scientific notation.
We use scientific notation because its no fun writing out 27 zeroes in a row in a number. Scientific notation lets us instead write “how many zeroes we have” as a power of 10.
For example, 300000000 = 3 x 108 (8 zeroes = 108). (That number is the speed of light.)
Many calculators have the ability to do scientific notation automatically using a dedicated “scientific notation” key that will somehow look like it’s a 10 raised to some power (EE or EXP key); if not, you can enter the multiply by 10 and the exponent (power) manually by typing “10 raised to the power 8 times 3”. Make sure you type that correctly if you’re doing it that way!
Spreadsheet programs also do this type of notation very rapidly. For example, if you have access to Microsoft Excel and haven’t done it before, type “3e8” into a cell and hit enter. You’ve just entered that same number.
For numbers that are smaller than 1, you use a negative exponent on the 10, as seen here.
0.00000005 = 5 x 10-8
Put these numbers into Scientific notation (2 points each):
(a) 342000000000
(d) 0.385926587
(b) 0.0000000000047
(e) 0.000034656
(c) 91000000000000
(f) 110000000000001
Take these numbers out of scientific notation and write them out (2 points each):
(a) 5.63 x 10-5
(f) 3.8 × 1010
(b) 2 x 104
(g) 3.48567 × 105
(c) 1.47 × 107
(h) 2 × 100
(d) 6.4545 × 10-8
(i) 2.2222222222 × 1012
(e) 4 × 103
(j) 3.45656 × 10-5
Part 5: The final part of this recitation involves practice with “units”. Here you’ll get a chance to work with the units scientists use, how to convert between them, and how scientific notation helps with doing so.
Scientists like using meters/kilometers/etc. because we can put them in scientific notation easily. These are called SI units and everything is done in factors of 10.
First as an introduction to units: Answer these questions to practice using units:
(a) 1 kilometer = 1000 meters. How many meters are in 100 kilometers? Write it in scientific notation (4 points).
(b) 1 meter = 1000 millimeters. How many kilometers are in 2 millimeters? Write both the decimal amount and write it in scientific notation (2 questions here, 8 points).
(c) Radio waves have a wavelength of 1 x 105 to 1 x 107 micrometers (m), where 1 micrometer = 10-6 meters. What is the wavelength range of radio waves in meters? (6 points)
(d) We showed earlier that the wavelength of orange to yellow visible light is about 600 nm. 1 nm = 1 nanometer = 10-9 meters. How does the wavelength of this type light compare to a radio wave with a wavelength of 106 m? (6 points)
(e) Here’s an exercise showing why scientists like SI units. The Radius of the planet Earth is 6371 kilometers. How many meters is that? (use scientific notation, 4 points).
(f) How many millimeters is that? (use scientific notation, 4 points).
(g) The radius of the Earth is 3959 miles. There are 5280 feet in a mile. How many feet is that? (do not use scientific notation, 4 points).
(h) There are 12 inches in a foot. How many inches is the radius of the Earth (again do not use scientific notation, 4 points).
(i) Now convert the number of inches in the Earth’s radius into scientific notation. What is easier to calculate, inches in the Earth’s radius or millimeters? (2 questions, 4 points total).
(j) This final exercise is called a factor label problem. To solve this problem you’ll have to convert a number of different measurements into an appropriate unit. One last thing you need: the speed of light is 3 x 108 meters per second (m/s).
The diameter of the sun is 1.4x1011 cm and the distance to the nearest star, Proxima Centauri, is 4.2 light years. Suppose you want to build an exact scale model of the sun and Proxima Centauri and you are using a ball 30 cm in diameter to represent the sun. In your scale model, how far away would Proxima Centauri be from the sun? Give your answer in kilometers. (15 points)
Could you build that scale model on the Earth? Yes or no. (4 points)
How many suns would it take, laid side-by-side, to reach Proxima Centauri? Give your answer in scientific notation. (5 points)
(a) 342000000000
(d) 0.385926587
(b) 0.0000000000047
(e) 0.000034656
(c) 91000000000000
(f) 110000000000001
Explanation / Answer
Put these numbers into Scientific notation (2 points each):
(a) 342000000000 = 3.42 x 1011
(b) 0.0000000000047= 4.7 x 10-12
(c) 91000000000000 = 9.1 x 1013
(d) 0.385926587 = 3.85 x 10-1
(e) 0.000034656 = 3.46 x 10-5
(f) 110000000000001=1.1 x 1014
Take these numbers out of scientific notation and write them out (2 points each):
(a) 5.63 x 10-5= 0.0000563
(b) 2 x 104 = 20000
(c) 1.47 × 107=14700000
(d) 6.4545 × 10-8=0.000000064545
(e) 4 × 103=0.004
(f) 3.8 × 1010=38000000000
(g) 3.48567 × 105=348567
(h) 2 × 100= 2
(i) 2.2222222222 × 1012 = 2222222222200
(j) 3.45656 × 10-5=0.0000345656
Part 5: The final part of this recitation involves practice with “units”. Here you’ll get a chance to work with the units scientists use, how to convert between them, and how scientific notation helps with doing so.
Scientists like using meters/kilometers/etc. because we can put them in scientific notation easily. These are called SI units and everything is done in factors of 10.
First as an introduction to units: Answer these questions to practice using units:
(a) 1 kilometer = 1000 meters. How many meters are in 100 kilometers? Write it in scientific notation (4 points).
Answer: 100 x 1000 = 1 x 105 meters
(b) 1 meter = 1000 millimeters. How many kilometers are in 2 millimeters? Write both the decimal amount and write it in scientific notation (2 questions here, 8 points).
Answer: 2 mm x 0.001 m x 0.001 km = 2 x 10-6 km = 0.000002 km
(c) Radio waves have a wavelength of 1 x 105 to 1 x 107 micrometers (m), where 1 micrometer = 10-6 meters. What is the wavelength range of radio waves in meters? (6 points)
Answer: 1 x 105 mx 10-6 m/m = 1 x 10-1 m
1 x 107 mx 10-6 m/m = 1 x 10 m
The wavelength range is 0.1 m to 10 meters
(d) We showed earlier that the wavelength of orange to yellow visible light is about 600 nm. 1 nm = 1 nanometer = 10-9 meters. How does the wavelength of this type light compare to a radio wave with a wavelength of 106 m? (6 points)
Answer: (there are MANY types of comparison, but we can stablish the following)
600 nm = 6 x 10-7 m
106 m = 1 m. The wavelength of the yellow light is 0.0000006 times the wavelength of a radio wave.
(e) Here’s an exercise showing why scientists like SI units. The Radius of the planet Earth is 6371 kilometers. How many meters is that? (use scientific notation, 4 points).
Answer: 6371 km x 1000 m/km = 6371000 =6.37 x 106 m
I will gladly answer the other parts if you post them on a new question.
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