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Stuff on Arithmetic and Units

No, numbers with unlike units cannot be added or subtracted. Yes, of course numbers with like units can be added and subtracted. Yes, numbers with unlike units can be multiplied and divided. Each unit stays in the answer. This particular example yields a

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Stuff on Arithmetic and Units

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  1. No, numbers with unlike units cannot be added or subtracted Yes, of course numbers with like units can be added and subtracted Yes, numbers with unlike units can be multiplied and divided. Each unit stays in the answer. This particular example yields a weird and un-useful derived unit. Yes, numbers with like units can be multiplied. Useful squared and cubed derived units can result depending upon the unit. What happened to the units? Stuff on Arithmetic and Units Can we do this: 1 .00 ft + 3 in = ???? How about this: 1.00 ft + 0.25 ft = 1.25 ft Can we do this: 1.00 ft x 3 in = 3 ft-in And this… 1.00 ft x 0.25 ft = 0.25 ft2 And this… 1.00 ft  0.25 ft = 4.00

  2. We always say “B cancels”. What does that mean? B It means, = 1 and 1 multiplied by B by any value does not change the value. AB 1 A = CD B CD ) ( ( ) 1.00 atm x 10.0 L 300. K 1 = 200. atm 1.67 x 10-4 L/K More on Arithmetic and Units • Have you noticed yet that units can be multiplied and divided just like numbers or variables? They act like numbers or variables and are manipulated separately from them. • EXAMPLE: Units…. Where did the atm unit go? It “canceled” because atm/atm = 1

  3. 1 ft 12 in = 1 ft 1 ft • = 12 in • 1 ft Dimensional AnalysisMethod for converting from one unit to another FACT: Any expression can be multiplied by 1 without changing its value. So…What is 1 anyway ? Consider: 1 ft = 12 in Isn’t this fraction equal to 1, too? This is an example of a conversion factor

  4. = 1 ft • 12 in • = 1 ft • 12 in • = 12 in • 1 ft • = 12 in • 1 ft Conversion Factors Suppose we flip it or invert it? The inverted fraction is still equal to 1. Ok, now we have TWO conversion factors for changing from feet to inches or inches to feet. AND

  5. 1 ft 12 in 12 in 1 ft More on Conversion Factors The VALUE of that distance is the same whether I say it is 1 foot or 12 inches. (A carpenter can use 1 ft or a 12 inch board for the same job.) How many inches in 42.7 feet? Multiply 42.7 feet by the correctconversion factor: Now, 42.7 ft has the same value as 512 in. The units are just different. (42.7 ft) = 512 in

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