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OBJECTIVE September 9, 2013 In our study of SCIENTIFIC NOTATION (Supporting) the students will be able to Express numbers in standard form (COMPREHENSION) and show what they learned by Converting Numbers. (COMPREHENSION) SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS. Examples of REALLY BIG NUMBERS! 100 quadrillion cells make up the human body The largest known number that can't be expressed in terms of any smaller numbers, aka a PRIME NUMBER, was discovered in 2008, is 243,112,609 . The total number of Which is a number with nearly particles in the universe, is 13 million digits generally thought to be around 1080 ! Examples of NUMBERS. really, really small •the charge on an electron: roughly 1.6 × 10-19 C (negative) Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers. Scientific Notation A number is expressed in scientific notation when it is in the form ax n 10 where a is between 1 and 10 and n is an integer Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why? To change a # to scientific notation Ex. 1,530,000 Steps 1.put decimal between #’s so you get a # between 1 and 10 it can NOT be bigger than 10 (The amount has to be greater than $1, but less than $10!) 2. how many places you moved the decimal is the exponent Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. Ex. 1,530,000 1.53 x 10 6 45620 .00236 2.36 x 10 -3 4 4.562 x 10 Ex. 0.000 000 000 753 kg 7.53 10 10 This is the mass of a dust particle! Ex 7,100,000,000 7.1 10 9 This is the distance from Earth to Pluto in miles Example 3 Given: 289,800,000 Move the decimal: 2.898 (moved 8 places) Answer: 2.898 x 108 Example 4 Given: 0.000567 Move the decimal: 5.67 (moved 4 places) Answer: 5.67 x 10-4 Why does a Negative Exponent give us a small number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 Do you see a pattern? The nucleus of a human cell is about 0.00000704 meters in diameter. What is the length in scientific notation? 7.04 X -6 10 A ribosome, another part of a cell, is about 0.00000000375 of a meter in diameter. Write the length in scientific notation. -9 3.75 X 10 Practice – Convert from Standard Form to Scientific Notation 1. 2. 3. 4. 5. 0.1333 60000000 23450 0.007904 0.0000035093 1) Decide whether the number is in scientific notation. If not, tell why the number is not in correct scientific notation a. 0.54 x 103 b. 2.2 x 100.3 c. 800 x 105 2) Write the following numbers using scientific notation: a. 7234 b. 0 .085 c. 1.11 Write in scientific notation. 1. 0.0053 = 2. 634,000 = 3. 55,600,000 = Changing scientific notation to standard form. To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.) Example 3 Given: 6 10 5.093 x Answer: 5,093,000 (moved 6 places to the right) Example 4 Given: -4 10 1.976 x Answer: 0.0001976 (moved 4 places to the left) Practice 1. 2. 3. 4. 5. 5 10 1.493 x -4 2.908 x 10 2 3.90284 x 10 -1 1.333 x 10 7 6.0000009 x 10 Practice 6. 7. 8. 9. 10. 2.345 x 104 0 4.50000 x 10 -3 7.904 x 10 3.5093 x 10-6 -2 2.309 x 10 Additional Example : Life Science Application A human skin cell has a diameter of approximately 4.11 x 10-5 meters. A cell from the liver has a diameter of 1.5 x 10-5 meters. Which cell has a greater diameter? 4.11 x 10-5 1.5 x 10-5 10-5 = 10-5 Compare powers of 10. 4.11 > 1.5 Compare the values between 1 and 10. 4.11 x 10-5 > 1.5 x 10-5 The first cell has a greater diameter. 1. 5.3 X -3 10 = 6.34 X 5 10 = 3. 5.56 X 7 10 = 2. Even More Practice Below is a list of links to games and activities all having to do with scientific notation. – http://www.aaamath.com/dec71idec2sci.html – http://janus.astro.umd.edu/cgibin/astro/scinote.pl – http://www.sciencejoywagon.com/physicsz one/lesson/00genral/dectosci.htm Now take the quiz to test your scientific notation skills! Click on the link below to take the quiz and then use the answer key for the correct answers. – Quiz – Answers Changing standard form to scientific notation. http://www.youtube.com/watch?v=HtXTKrigYqk&feature=relmfu