Warm up – August 14, 2017 How many significant digits are in the following numbers and what are they? Number Sig fig Which ones 81 26.2 0.007 5200.38 380.0 78800 78800.

Warm up – August 14, 2017 How many significant digits are in the following numbers and what are they? Number Sig fig Which ones 81 2 8,1 26.2 3 2,6,2 0.007 1 7 5200.38 6 5,2,0,0,3,8 380.0 4 3,8,0,0 78800 7,8,8 78800. 5 7,8,8,0,0

Monday, August 14, 2017 Turn in homework Check sig fig foldable Notes on Scientific notation & dimensional analysis Scientific notation foldable Dimensional analysis homework

Interactive Notebook Table of Content Left Side Page Right Side Scientific notation foldable 14 Scientific notation & dimensional analysis notes 15 Why is scientific notation used?

Scientific notation Scientific notation is used to express very large or very small numbers 2 parts Number between 1 and 10 x 10 to an exponent The exponent can be determined by the number of decimal places you have to move to get only 1 number in front of the decimal

Large Numbers If starting number is greater than 1 the exponent will be positive. Example: 39923 (steps) Move decimal until 1 number is in front: 3.9923 Now add x10: 3.9923 x 10 Now count the number of decimal places that you moved: 4 Since number is greater than 1 the exponent will be positive : 3.9923 x 104

Small numbers If the number you start with is less than 1, the exponent will be negative. Example: 0.0052 Move decimal until 1 number is in front: 5.2 Now add x10: 5.2 x 10 Now count the number of decimal places that you moved: 3 Since number is less than 1 the exponent will be negative: 5.2 x 10-3

Going from Scientific notation to standard notation You start with the number and move the decimal the same number of spaces as the exponent. If the exponent is positive, the number will be greater than 1 If the exponent is negative the number will be less than 1. Example: 3 x 106 5 x 10-4

Dimensional analysis When we measure something, we always specify what units we are measuring in. All kinds of units are possible, but in science we use the SI system Problem! What if I measure something in inches but I am supposed to give you the answer using SI units?

Converting between different standards of measurement How many seconds are in a day? How many inches are in a centimeter? If you are going 50 miles per hour, how many meters per second are you traveling? To answer these questions you need to change (convert) from one unit to another.

How do you change units? Whenever you have to convert a physical measurement from one dimensional unit to another, dimensional analysis is the method used. Dimensional analysis – converting from one unit system to another.

How does dimensional analysis work? In order to perform any conversion, you need a conversion factor. Conversion factors are made from any two terms that describe the same or equivalent “amounts” of what we are interested in. Examples: 1 inch 2.54 cm 1 miles 5,280 feet 60 minutes 1 hour 24 hours 1 day 100 cm 1 m 12 inches 1 foot 16 ounces 1 pound

Steps of dimensional analysis (copy step in INB) All dimensional analysis problems are set up the same way. They follow this same pattern: Identify starting and ending units Line up conversion factors so units cancel Multiply all top numbers and divide by each bottom number Check units and answer What units you have x What units you want = What units you want What units you have The units you want to end with The number & units you start with The conversion factor (The equality that looks like a fraction)

Example Problem How many feet are in 60 inches You need a conversion factor. Something that will change inches into feet. Remember 12 inches = 1 foot Written as an “equality” or “ratio” it looks like 60 inches 5 feet x = (Mathematically all you do is: 60 x 1  12 = 5) What units you have x What units you want = What units you want What units you have

Example Problem #2 You need to put gas in the car. Let's assume that gasoline costs $3.35 per gallon and you've got a twenty dollar bill. How many gallons of gas can you get with that twenty? Try it! $ 20.00 1 gallon = 5.97 gallons $ 3.35 (Mathematically all you do is: 20 x 1  3.35 = 5.97)

Example Problem #3 You have a twenty dollar bill and you need to get gas for your car. If gas is $3.35 a gallon and your car gets 24 miles per gallon, how many miles will you be able to drive your car on twenty dollars? Try it! $ 20.00 1 gallon 24 miles = 143.28 miles $ 3.35 1 gallon (Mathematically all you do is: 20 x 1  3.35 x 24  1 = 143.28 )

Scientific notation foldable