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Chapter 2

Chapter 2. Scientific measurement. Types of measurement. Quantitative - uses or refers to a standard (numerical measurements) Qualitative - use description without reference to a standard 40 cm large Hot 100ºC. Scientists prefer. Quantitative- easy to check

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Chapter 2

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  1. Chapter 2 Scientific measurement

  2. Types of measurement • Quantitative- uses or refers to a standard (numerical measurements) • Qualitative- use description without reference to a standard • 40 cm • large • Hot • 100ºC

  3. Scientists prefer • Quantitative- easy to check • Easy to agree upon, no personal bias • The measuring instrument limits how good the measurement is

  4. How good are the measurements? • Scientists use two word to describe how good measurements are • Accuracy- how close the measurement is to an accepted value • Precision- how well can the measurement be repeated (are the readings closely grouped)

  5. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it • examples

  6. Let’s use a golf analogy

  7. Accurate? No Precise? Yes

  8. Accurate? Yes Precise? Yes

  9. Precise? No Accurate? No

  10. Accurate? Yes Precise? We cant say!

  11. In terms of measurement • Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?

  12. 1 2 3 4 5 Significant figures (sig figs) • Are the digits in a numerical measurement that have meaning (were measured) • When we measure, we always estimate between the smallest divisions. What is the length? The length may be recorded as: 4.5, 4.6 or 4.7 cm (estimated digit) (Variation is .1 cm) The value of the estimate is not known with certainty

  13. Significant figures (sig figs) • The smaller the divisions the better we can estimate (readings are more closely grouped). • Scientist understand that the last digit in a measurement is an estimate What is the length? Length may be recorded as: 4.53, 4.54 or 4.55 cm (estimate) (Variation is .01 cm) Compare this grouping to the previous slide. 1 2 3 4 5

  14. Sig Figs • What is the smallest mark on the ruler that measures 142.15 cm? • 142 cm? • 140 cm? • All nonzero digits in a measurement are significant (have meaning – were measured or estimated) • There is a problem, does a zero count or not? Was the zero measured or is it a place holder? • You need a set of rules to decide which zeroes count as measured (are significant digits) and which are place holders (do not count as significant digits).

  15. Which zeros count? • If the measurement is a number with a decimal point count from left to right starting at the first nonzero. (DR) • 0.045 Two sig figs (two zeroes are place holders) • If a measurement is expressed as a number with no decimal point shown, you start to count the number of significant digits from right to left. The count starts at the first nonzero digit. (NDL) • 12400 Three sig figs (two zeroes are place holders)

  16. Which zeros count? State the number of sigfigs in each of the following: • 1002 m • 45.8300 cm • 0.0000001500 m • 15020100 km 4 sig fig 6 sig fig 4 sig fig 6 sig fig

  17. Sig Figs All measurements have two components: numerical (sig figs.) and the dimension (unit). Sig fig rules do not apply to: counting numbers or defined numbers. Counted numbers are exact. A dozen is exactly 12. Defined numbers are exact. 1 m is 100 cm. Being able to locate, and count significant figures is an important skill.

  18. Sig figs. How many sig figs in the following measurements? 458 g 3 sig fig 4085 g 4 sig fig 4850 g 3 sig fig 0.048 g 2 sig fig 4.0485 g 5 sig fig 40.40 g 4 sig fig

  19. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.5060 g 4 sig fig 3 sig fig 3 sig fig 6 sig fig 4 sig fig Next we learn the rules for calculations

  20. Problems • 50 is only 1 significant figure • But if it really has two, how can it be written to show that both digits are significant? • A zero at the end only counts after the decimal place. If we use Scientific notation 5.0 x 101 the zero counts. (2 sig figs)

  21. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate (not known with certainty). Measurements can only have one estimated digit. • The answer, when you add or subtract, can not be better than your worst estimate. • have to round the answer to the place value of the measurement (in the problem) with the greatest uncertainty.

  22. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

  23. Rounding rules • Look at the digit in the place value following the one you’re rounding. • If the first digit to be cut is 0 to 4 don’t change it (round down) • If the first digit to be cut is 6 to 9 make it one bigger (round up) • If the first digit to be cut is exactly 5 (followed by nothing or zeros), round the number so that the preceding digit will be even. • Round 45.462 cm to: four sig figs to three sig figs to two sig figs to one sig fig 45.46 cm 45.5 cm 45 cm 50 cm

  24. Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 103 - 3.8 x 102 5.4 - 3.28 6.7 - .542 500 -126 6.0 x 10-2 - 3.8 x 10-3 11.6765 = 11.7 614.98 = 610 2.1175 = 2.118 6.0x103-.38x103=5.62x103=5.6x103 2.12 = 2.1 6.158 = 6.2 374 = 400 56.2x10-3 = 5.6x10-2

  25. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least number of s.f. in the question • 3.6 cm x 653 cm = 2350.8 cm2 • 3.6 cm has 2 s.f. 653 cm has 3 s.f. • answer can only have 2 s.f. • The rounded answer is 2400 cm2

  26. Multiplication and Division • The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. • 425 3 sf • x 11 2 sf • 425 • 425 • 4675 = 47002 sf • Round answer to have 1 uncertain digit =4700 • The product has the same number of significant digit as the least number in the multiplication

  27. Multiplication and Division • The rule is the same rules for division. • Practice 0.72056 = 0.72 28.1025 = 28 4.246852 = 4.2 0.001955 23.17507 = 23.2 4.5 / 6.245 4.5 x 6.245 9.8764 x 0.43 3.876 / 1983 16547 / 714

  28. The Metric System An easy way to measure

  29. Measuring Measurements involve two components: a number and a unit. The number is only part of a measurement It is 10 long 10 what. Numbers without units are meaningless.

  30. The Metric System is used because it is a decimal system Every unit conversion is some power of 10. A metric unit has two parts • A prefix and a base unit. The prefix tells you how many times to divide or multiply by 10.

  31. Base Units • Length - meter - m • Mass - grams – (about a raisin) – g Kg • Time - second - s • Temperature - Kelvin orºCelsius K orºC • Energy - Joules- J • Volume - Litre - L • Force Newton (N)

  32. Prefixes • kilo k 1000 times 103 • deci d 1/10 10-1 • centi c 1/100 10-2 • milli m 1/1000 10-3 • kilometer – 1000 m • centimeter - 1/100 m (100 cm = 1 m) • millimeter - 1/1000 m (1000 mm = 1 m)

  33. Volume • 1 L = 1000 cm3 = 1000mL • 1/1000 L = 1 cm3 • 1 mL = 1 cm3

  34. Mass • is the amount of matter. • 1gram is defined as the mass of 1 cm3 of water at 4 ºC. • 1000 g = 1000 cm3 of water • 1 kg = 1 L of water

  35. k h D d c m Converting • how far you have to move on this chart, tells you the power of ten, and which sign to use with the power of ten. • The box is the base unit, meters, Liters, grams, etc.

  36. k h D d c m Conversion Factors Change 5.6 m to millimeters start at the base unit and move three to the right. The power of ten is +3 = 1000. We want to change the units not the value, so we must multiply by 1. 5.6m x 1000 mm = 5600mm (the ratio=1) 1m

  37. Conversion Factors The units of measurement are not always convenient dimensions and it may become necessary to change units. In a lab the distance could only be measured in cm. To calculate the speed the cm must be converted to m without changing the value of the measurement. Distance in cm x [conversion factor] = distance in m

  38. Conversion Factors The only number that can multiply any other number without changing the number’s value is 1. The conversion factor is a ratio. The value of the ratio is 1. For the ratio to have a value of one the top term has to equal the bottom term. Start with 1255cm, want to find the number of m, then: By definition 1m = 100 cm 1 m = 1 100cm  1255 cm x 1 m = 12.55m 100cm The conversion factor must cancel the present unit and introduce the desired unit

  39. k h D d c m Conversion Factors convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters

  40. The solutions for some problems contain multi-steps (require more than one calculation to solve). Using Dimensional Analysis can solve this type of problem. Dimensional Analysis   Identify the given or known data (information).   Identify the unknown. Plan the solution or calculations by either: setting up a series of conversion factors OR using a formula. Check your work by canceling out units.  1. Calculate the number of seconds of Physics class there is in a week. The density of gold is 19.3 g. cm3 What is the density of gold expressed in kg? m3

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