Scientific Notation, Converting Units, and Magnitudes

Name: Stanley Nicholas Scientific Notation, Converting Units, and Magnitudes 1) Write the following numbers in scientific notation. 200 = 2.0 x 10 2 1500 = 1.5 x 10 -3 40,000 = 4.0 x 10 4 9,000,000 = 9 x 10 6 14 = 1.4 x 10 1 71050 = 7.1050 x 10 4 0.017 = 1.7 x 10 -2 0.003 = 3 x 10 -3 0.0000005 = 5 x 10 -7 0.00205 = 2.05 x 10 -3 2) List which number is the largest and estimate how much larger it is. No calculators allowed! Example: 9.5 x 10 4 , 9.0 x 10 6 : 9.0 x 10 6 is about 10 6-4 = 10 2 = 100 times larger than 9.5 x10 4 2.3 x 10 3 , 3.0 x 10 1 : 2.3 x 10 3 is about 10 3-1 = 10 2 = 100 times larger than 3.0 x 10 1 8.7 x 10 8 , 7.8 x 10 4 : 8.7 x 10 8 is about 10 8-4 = 10 4 = 10,000 times larger than 7.8 x 10 4 Entering Scientific Notation in a Calculator It is very important that you know how to use scientific notation on your calculator. There are several possible buttons that are the code for scientific notation: EE, x10 x ,. EXP. If your calculator doesn’t have one of these 3 buttons, please call me over so we can find the right button. It is important that you follow these steps exactly: a) First enter whatever is before the “x” in your number. b) Then press your scientific notation button. c) Finally enter your exponent. Note: You do NOT want to hit the “x” button when putting a number in scientific notation.

Example: 4.2 x 10 8 a) Enter 4.2 b) Press scientific notation button c) Enter 8 (your exponent) 3) Write out the buttons that you would press to enter the following in scientific notation: a) 9.20 x 10 3 = 9.2 EXP 3 b) 6 x 10 2 = 6 EXP 2 c) 4.2 x 10 -4 = 4.2 EXP -4 d) (5.1 x 10 9 ) / (1.5 x 10 7 ) = (5.1 EXP 9) / (1.5 EXP 7) 4) Use your calculator to solve the following problems. a) (5.1 x 10 9 ) x (9.3 x 10 2 ) = 4.743 x 10 12 b) (8.7 x 10 5 ) / (1.1 x 10 1 ) = 79,090.9091 c) In one second, light can travel 1.86 x 10 5 miles. In a year, there are 3.15 x 10 7 seconds. Calculate how many miles light travels in 1 year. Show your work! (1.86 x 10 5 ) x (3.15 x 10 7 ) = 5.859 x 10 12 miles Converting Between Units Sometimes you will have to convert between two units. For instance I may tell you a distance in kilometers but you need the distance in miles. Here are some examples to help you get an idea of how it works: a) Convert 3 meters (m) into centimeters (cm). Hint: 1 m = 100 cm 3 m x 100 cm = 300 cm 1 m b) Convert 3 meters (m) into kilometers (km). Hint: 1 km = 1000 m 3 m x 1 km = 0.003 km 1000 m

Apparent Magnitudes One important property of stars is its apparent magnitude. We will be learning the apparent magnitude for the alpha and beta stars of each constellation we study. Apparent magnitude measures how bright a star looks to us from Earth! The one tricky thing is that the smaller the number is, the brighter the star looks! 7) Answer the following questions about apparent magnitude. a) Put the following stars in order from the brightest in the sky to the faintest: Star Apparent Magnitude Regulus +1.35 Procyon +0.34 Nanhai +3.54 Procyon, Regulus, Nanhai b) Canopus has an apparent magnitude of -0.72. Will it be brighter or fainter than Procyon? Explain. Brighter because a negative magnitude smaller than a positive magnitude. c) Sirius has an apparent magnitude of -1.4 Will it be brighter or fainter than Canopus? Explain. Sirius will be brighter because -1.4 is smaller than -0.72 The apparent magnitude of a star tells us whether we will be able to see the star with our eyes. Location Stars Visible Downtown LA Apparent Magnitude < 2 Mt. SAC Campus Apparent Magnitude < 3 In a Park in Walnut w/ no bright lights nearby Apparent Magnitude < 4 Desert with no lights Apparent Magnitude < 5.5 to 6 d) Which of the following stars (Regulus, Procyon, Nanhai, Canopus, Sirius) will you be able to see: in Downtown LA: Sirius, Canopus, Regulus, Procyon on Mt. SAC campus: Sirius, Canopus, Regulus, Procyon

in the Desert: Sirius, Canopus, Regulus, Procyon, Nanhai e) In the desert you can see approximately 4,000 – 5,000 stars. However, there are 200 billion stars in our galaxy! Do most stars in our galaxy have apparent magnitudes that are larger or smaller than 6? Explain your answer. Most stars in our galaxy have apparent magnitudes that are larger than 6. Since it is required that stars have a smaller apparent magnitude of 5.5 to 6 to be visible in the desert and we are only able to see 4,000-5,000 stars out of 200 billion stars in the desert, that means there are more stars in our galaxy that have apparent magnitude larger than 6. For every difference in magnitude of 1, a star is 2.5x brighter. For example, if Star A has an apparent magnitude of 2 and Star B has an apparent magnitude of 3, Star A is 2.5x brighter than Star B. To calculate how many times brighter a star is, you can use the equation: # of times brighter = 2.5 (mag. of faint star – mag. of bright star) Example: Star C has a magnitude of 1. Star D has a magnitude of 4. Star C is 2.5 (4-1) = 2.5 3 = 15.6x brighter than Star D. To calculate 2.5 3 in a calculator, 1) Enter 2.5 2) Push either the x y or y x or ^ button 3) Enter exponent (in this case 3). 8) Answer the following questions about how many times brighter a star will be. a) Which star will look the brightest in the sky and how many times brighter will it look? Star Meg (apparent magnitude = 3) or Star Matt (apparent magnitude = 7). 2.5 (7-3) = 2.5 4 = 39.0625 Star Meg is 2.5 (7-3) = 2.5 4 = 39.0625x brighter than Star Matt b) Which star (Regulus or Nanhai) will look the brightest in the sky and how many times brighter will it look? Regulus is 2.5 (3.54-1.35) = 2.5 2.19 = 7.439x brighter than Nanhai c) Which star (Regulus or Sirius) will look the brightest in the sky and how many times brighter will it look? Sirius is 2.5 (1.35+1.4) = 2.5 2.75 = 12.426x brighter than Regulus