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chapter 5 Measurements & Calculations

Learn about scientific notation, units of measurement, and significant figures in this chapter. Understand how to convert between different units and solve problems using dimensional analysis.

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chapter 5 Measurements & Calculations

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  1. chapter 5Measurements & Calculations Warning!Lots of math(not tough math, but lots of it)

  2. Remember there are qualitative and quantitative observations • This chapter deals with the quantitative! called measurements

  3. these measurements are not just numbers • they have units • as in5 millimeters,75 people,16 mph, etc. • but first…

  4. 5.1 scientific notation • Some numbers are just too darn big or too small to deal with reasonably • Scientific Notationis a method for making very large or very small numbers more compact and easier to write. • as in: 64,400,000,000 can be written 6.44 x 1010 • it’s easy! :)

  5. Description:scientific notation must be written as the product of a number between 1 and 10 and the appropriate power of 10 • just count how many times you have to move the decimal point to get a number between 1 and 10 • if the number is gettingsmaller the exponent willcompensate by gettingbiggerand vice versa

  6. examples • 238,000 2.38 x 105 • 1,500,000 1.5 x 106 • 0.00043 4.3 x 10-4 • 0.135 1.35 x 10-1 • 357 3.57 x 102

  7. 5.2 units • go into a restaurant, sit down, just tell the waitress “two,” and see what you get • Units are used everyday to give meaning to numbers • people have used them since, like, forever…

  8. the English system is used in the US; the metric system is used everywhere else • scientists everywhere use metric and standardized it into the International System (SI)

  9. these are the basic units of SI • know them,love them,marry them

  10. and these are the prefixes we use to make them even more convenient • “1 mm” is easier to use & write than “one thousandth of a meter” • know them, love them, marry them m

  11. 5.3 measurements of length, volume, and mass • length is based on the meter

  12. volumeis how much 3D space something takes up • SI unit is the m3 • one thousandth of that is the dm3, aka the liter • 0.001 of that is cm3 or ml

  13. we mostly measure volume with a graduated cylinder but also these critters, all of which are marked on the side

  14. Remember that when you use the Graduated cylinder to read the bottom of the meniscus

  15. mass is measured in grams (even though SI unit is kg) • measured with a balance

  16. this is a table to get you better acquainted with it all

  17. 5.4 uncertainty in measurement • many measurements are made of objects that make us estimate • so, we’ll always argue about the last number or two • the ones we agree on are called certain, the argued ones uncertain

  18. 31.7 31.8 31.8 31.6 31.7 31.7 31.8 31.6 • every measuring device has some degree of uncertainty • the certain numbers+the one uncertain one are called significant…

  19. which instrument gives us more sigfigs? • that’s the one you want to use (but it probably costs a lot more!)

  20. 5.5 significant figures • the whole rest of your science/math life must reflect the measuring devices so you’se all gotta know dese tings called sigfigs • so what about zero’s and what not? • there are rules! yippee! ready?

  21. one more thing…

  22. examples • the mass of an eyelashis 0.000304 g • 3 • the length of the skidmark was 1.270 x 102 m • 4 • A 125-g sample of chocolate chip cookie contains 10 g of chocolate • 3, 1 • the volume of soda remaining in a can after a spill is 0.09020 L • 4 • a dose of antibiotic is 4.0 x 10-1 cm3 • 2

  23. rounding off • yes, there are rules even for this • remember to use only the first digit to the right of the last sigfig to help you decide

  24. determining sigfigs in calculations • there are only two basic rules here, one to do with multiplication and division, the other addition and subtraction…

  25. Multiplying and dividing • answer will have as many sigfigs as the working number w/ the fewest • examples • 2.34 • 3.2 = 7.488? • smallest number of s/d is 2 so 7.5 • 35.0 / 6.734 = 5.1975051975? • smallest number of s/d is 3 so 5.20

  26. addition and subtraction… • first add them up! don’t worry about sigfigs until the end! • 3.75 + 4.1 = 7.85 • you can only go to where all numbers have something to contribute, so can only go to7.8 • 3.987 + 4.60 = 8.587 • but can only go to 0.01, so 8.59

  27. 5.6 problem solving and dimensional analysis • I have to buy 72 CostCo muffins, but they only sell them by the dozen. Do I just give up? May it never be! • I convert into dozens! • but I have to know the relationship b/t individuals and dozens! • called a conversion factor! • here 1 dozen = 12

  28. unit1x conversion factor = unit2 • we’ll…1) make astarting point,2) determinewhere we’re going,then…3) build a bridgeto it with theconversion factor

  29. 1) write down what you know (given),2) where you’re going, then3) build a Bob/Eddie bridge (your book calls the bridge an equivalence statement) between them… • Change 100 mm into m. bridge where you’re going given 100mm x 1 m 0.1 = m BOB  1000 mm EDDIE

  30. Change 546 cm into mm. bridge where you’re going given 546cm x 10 mm 5460 = mm BOB  1 cm EDDIE

  31. Convert 7.75g to µg. bridge where you’re going given µg 7.75g x 106 7.75x106 or 7,750,000 = µg  g 1

  32. Change 45mm into km. • (Hint: you might make this a 2-stepper.) 1 km 45mm 1 m = 1000 m 1000 mm 4.5x10-5 or .000045 km

  33. 5.7 temperature conversions:an approach to problem solving • here we learn both the different temp scales and how to convert between them

  34. the Big Three Temp Scales are Fahrenheit, Celsius, and Kelvin • in science we use almost exclusively C and K

  35. converting between K and C • a degree C and K are the same amount; they just differ by their starting points • they only differ by 273 • thus, and simply • TC + 273 = TK

  36. examples • What is 70˚C in kelvins? • TC + 273 = TK • 70 + 273 = 343 K • Nitrogen boils at 77 K. What is that in C? • TC + 273 = TK • TC = TK - 273 • TC = 77 - 273 • TC = -196 ˚C

  37. converting between F and C • here we have different size units and different starting points! yikes! • short story:TF = 1.80TC + 32

  38. examples • It’s 28˚C outside. What is that in F? • TF = 1.8TC + 32 • TF = 1.8(28) + 32 • TF = 50. + 32 • TF = 82 ˚F • It’s -40˚C in that lab freezer. What’s that in F? • TF = 1.8TC + 32 • TF = 1.8(-40) + 32 • TF = -72 + 32 • TF = -40˚F (!)

  39. examples • You have a 101˚F fever. What is that in C? • TF = 1.8TC + 32 • 101 = 1.8TC + 32 • 69 = 1.8TC • 38 = TC • Page 142 has a bunch of cutesy conversion equations

  40. 5.8 density • density is just how much stuff is crammed into a certain space • in science speak it’s mass/volume: D = m/V • finding mass is no problem; how do you find volume?

  41. one can either use dimensions (like lxwxh) or volume displacement for irregular objects • take volume before, volume after - tada!the difference is the volume of your object

  42. d.m.v helper m D V

  43. d.m.v helper m D V

  44. d.m.v helper m D V

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