Do Now 5 Minutes. Topic Scientific Notation. State how many significant figures are in each of the following numbers. How do you know?
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1 Do Now 5 Minutes Topic Scientific Notation State how many significant figures are in each of the following numbers. How do you know? 1, ,000,000,000, ,000,000, Is there a better way to display these numbers?
2 Homework Complete the Significant Figures, Scientific Notation, and Dimensional Analysis Worksheet. Due 9/19/14 All Physics Homework will be due on D Days
3 Significant Figures Initial Zeroes Captive Zeroes Terminal Zeroes Initial Zeroes are NEVER counted. Captive Zeroes are ALWAYS counted. Terminal Zeroes are sometimes counted. Only counted if there IS a decimal point.
4 Scientific Notation In Science, we tend to use big numbers: The speed of light: c = 300,000,000 m/s Newton s Gravitational Constant: G = N (m/kg) Avogadro s Number: (the number of molecules in a mole of substance) 602,000,000,000,000,000,000,000
5 Scientific Notation Imagine you are writing a paper using Avogadro s Number, how it was measured, and if the number is accurate or not. It would be very annoying to write out 602,000,000,000,000,000,000,000 over and over again, right? Fortunately, we can use Scientific Notation to simply our lives.
6 Scientific Notation Scientific Notation is a way to write very large or small numbers easily. Typical Scientific Notation looks like: a x 10 b We would read that as, a times ten to the power of b.
7 Scientific Notation Using Scientific Notation, we can re-write the speed of light as: c = 3 x 10 8 m/s Newton s Gravitational Constant: x N (m/kg) Avogadro s Number: 6.02 x mol -1 Those are much easier to work with.
8 Scientific Notation It is the convention to show your number as N.NN x 10 E where N is a number and E is the exponent. You should keep 1 digit before the decimal place. Is this written correctly? x 10 3 No. It should be: x 10 5
9 Scientific Notation Sometimes you will see a negative number instead of a positive number in the exponent. Describe what that means/signifies. When converting a number, if you have to move the decimal point to the left, the sign is positive. If you move it to the right, it gets a negative sign.
10 Scientific Notation Decimal point: Moves to the left: positive sign Moves to the right: negative sign Number of times you move the decimal point = number you put in the exponent. Let s try some together now.
11 Scientific Notation Practice ,000 3,000,
12 Sci. Not. Arithmetic Take a moment now and get out your calculator. Quickly calculate by multiplication: 2,000,000,000,000,000,000,000 and 3,700,000,000,000,000,000,000,000,000,000 What about dividing: 8,000,000,000,000,000,000,000,000,000 by 2,000,000,000,000,000
13 Scientific Notation Seems annoying right? Fortunately, using Scientific Notation we can very easily simplify this daunting task.
14 Scientific Notation Step 1: Change the numbers into Scientific Notation What do 2,000,000,000,000,000,000,000 and 3,700,000,000,000,000,000,000,000,000,000 turn into? (2 x ) and (3.7 x )
15 Step 2: When Multiplying When multiplying two numbers in Sci. Not., multiply the N.NN terms to get their product. Step 3: Then add the numbers in the exponents together. (2 x ) and (3.7x10 29 ) What do our numbers turn into? (7.4 x )
16 Step 2: When Dividing When dividing two numbers in Sci. Not., divide the first N.NN by the second N.NN. Step 3: Then subtract the numbers in the exponents together. Let s try this now using our second set of numbers.
17 When Dividing 8,000,000,000,000,000,000,000,000,000 divided by 2,000,000,000,000,000:
18 When Adding The same is also true when adding and subtracting as well. We can very easily add: (4.216 x 10 6 ) + (5.351 x 10 6 ) Add the N.NN parts together: = If the exponents are the same = do nothing! (9.567 x 10 6 )
19 When Subtracting (7.913 x 10 4 ) - (5.695 x 10 4 ) Subtract the N.NN from each other: = If the exponents are the same = do nothing! (2.218 x 10 4 )
20 What If (6.468 x 10 4 ) + (3.224 x 10 5 ) Make the exponents the same, then proceed as you normally would. (6.468 x 10 4 ) + (32.24 x 10 4 ) How else could you have written that? ( x 10 5 ) + (3.224 x 10 5 )
21 Exit Slip Let s see how well you understood today s lesson: 1. (2.746 x 10 6 ) + (1.004 x 10 6 ) 2. (9.733 x 10 6 ) - (4.211 x 10 5 ) 3. (4.25 x ) x (2.0 x ) 4. (7.50 x ) / (2.50 x )
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