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PWISTA Math of Chemistry

PWISTA Math of Chemistry. Scientific measurement Accuracy and Precision Sig Figs Metric System. Types of measurement. Quantitative - use numbers to describe Qualitative - use description without numbers 4 feet extra large Hot 100ºF. Scientists prefer. Quantitative- easy check

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PWISTA Math of Chemistry

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  1. PWISTAMath of Chemistry Scientific measurement Accuracy and Precision Sig Figs Metric System

  2. Types of measurement • Quantitative- use numbers to describe • Qualitative- use description without numbers • 4 feet • extra large • Hot • 100ºF

  3. Scientists prefer • Quantitative- easy 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 the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated

  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? Maybe?

  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) • How many numbers mean anything • When we measure something, we can (and do) always estimate between the smallest marks.

  13. Sig Figs Significant digits, which are also called significant figures, are very important in Chemistry. Each recorded measurement has a certain number of significant digits. Calculations done on these measurements must follow the rules for significant digits.

  14. Sig Figs The significance of a digit has to do with whether it represents a true measurement or not. Any digit that is actually measured or estimated will be considered significant. Placeholders, or digits that have not been measured or estimated, are not considered significant. The rules for determining the significance of a digit will follow.

  15. Significant figures (sig figs) • The better marks the better we can estimate. • Scientist always understand that the last number measured is actually an estimate 1 2 3 4 5

  16. Sig Figs • What is the smallest mark on the ruler that measures 142.15 cm? • 142 cm? • 140 cm? • Here there’s a problem does the zero count or not? • They needed a set of rules to decide: which zeroes count? • All other numbers do count

  17. The Standard Rules 1) Digits from 1-9 are always significant. 2) Zeros between two other significant digits are always significant. (sandwich rule) 3) One or more additional zeros to the right of both the decimal place and another significant digit are significant. 4) Zeros used solely for spacing the decimal point (placeholders) are not significant.

  18. Too Confusing! Heads will spin!

  19. Alternate Rule for Significant Digits • Rules Courtesy of Fordham Prep website. • When you look at the number in question, you must determine if it has a decimal point or not.  If it has a decimal, you should think of "P" for "Present".  If the number does not have a decimal place, you should think of "A" for "Absent".

  20. Alternate Rule for Significant Digits • Example, for  the number 35.700, think "P", because the decimal is present. • For the number 6500, you would think "A", because the decimal is absent.

  21. Alternate Rule for Significant Digits • Now, the letters "A" and "P" also correspond to the "Atlantic" and "Pacific" Oceans, respectively.  • Assume the top of the page is North, and imagine an arrow being drawn toward the number from the appropriate coast.  • Once the arrow hits a nonzero digit, it and all of the digits after it are significant.

  22. Example 1   How many significant digits are shown in the number 20 400 ?  (remember that we use spaces, rather than commas, when writing numbers in Science. Well, there is no decimal, so we think of "A" for "Absent".  This means that we imagine an arrow coming in from the Atlantic ocean, as shown below; 20 400 

  23. Example 1 The first non-zero digit the arrow hits would be the 4, making it, and all digits to the left of it significant.There are 3 significant digits20400 

  24. Example 2 How many significant digits are shown in the number 0.090 ?

  25. Example 2 • Well, there is a decimal, so we think of "P" for "Present".  This means that we imagine an arrow coming in from the Pacific ocean, as shown below; • 0.090

  26. Example 2 0.090 • The first nonzero digit that the arrow will pass in the 9, making it, and any digit to the right of it significant.

  27. Answer Example 2 • There are 2 significant digits in the number 0.090 • Here are the significant digits, shown in boldface.  0.090

  28. Which zeros count? • Those at the end of a number before the decimal point don’t count • 12400 • If the number is smaller than one, zeroes before the first number don’t count • 0.045

  29. Which zeros count? • Zeros between other sig figs do. • 1002 • zeroes at the end of a number after the decimal point do count • 45.8300 • If they are holding places, they don’t. • If they are measured (or estimated) they do

  30. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • A a piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill.

  31. Sig figs. • How many sig figs in the following measurements? • 458 g • 4085 g • 4850 g • 0.0485 g • 0.004085 g • 40.004085 g

  32. Sig Figs. • 405.0 g • 4050 g • 0.450 g • 4050.05 g • 0.0500060 g • Next we learn the rules for calculations

  33. ProblemsSame # - Different # sig figs … • 50 is only 1 significant figure • if it really has two, how can I write it? • A zero at the end only counts after the decimal place • Scientific notation • 5.0 x 101 • now the zero counts.

  34. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • have to round it to the least place of the measurement in the problem

  35. 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

  36. Rounding rules • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  37. Adding and Subtracting • RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

  38. We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g add 3.76 g + 14.83 g + 2.1 g = 20.69 g

  39. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3

  40. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 • Calculated answer = 2350.8 • 3.6 has 2 sig figs, 653 has 3 sig figs • answer can only have 2 sig figs • 2400

  41. Multiplying and Dividing • RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.

  42. EX: 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3 • We look to the original problem and check the number of significant digits in each of the original measurements: • 22.37 shows 4 significant digits. • 3.10 shows 3 significant digits. • 85.75 shows 4 significant digits.

  43. EX: 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3 • Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. • 5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. • Our final answer becomes 5950 cm3.

  44. Multiplication and Division • Same rules for division • practice • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714

  45. The Metric System An easy way to measure

  46. Measuring • The numbers are only half of a measurement • It is 10 long - - - 10 what? • Numbers without units are meaningless. • I’ll pay you 100 to mow the lawn … then give the person 100 cents. Won’t make friends that way.

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

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