1 Scientific Measurement, Significant Figures and Conversions Turning optical illusions into scientific rules

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

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

4 How good are the measurements? l Scientists use two words to describe how good the measurements are l Accuracy- how close the measurement is to the actual value l Precision- how well can the measurement be repeated

5 Differences l Accuracy can be true of an individual measurement or the average of several l Precision requires several measurements before anything can be said about it l 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 can’t say!

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

12 Significant figures (sig figs) l How many numbers in a measurement means something l When we measure something, we can (and do) always estimate between the smallest marks

13 Significant figures (sig figs) l The better marks the better we can estimate. l Scientist always understand that the last number measured is actually an estimate 21345

14 Sig Figs l What is the smallest mark on the ruler that measures cm? l One tenth of a cm l 142 cm? l 10 cm l 140 cm? l 100 cm l Here there’s a problem does the zero count or not? l They needed a set of rules to decide which zeroes count. l All other numbers do count

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

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

17 Sig figs. l How many sig figs in the following measurements? l 458 g l3l3 l 4850 g l3l3 l g l3l3 l g l9l9

18 More Sig Figs

19 Problems l 50 is only 1 significant figure l if it really has two, how can I write it? l 50.

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

21 For example l First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place

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

23 Practice l l = 11.7 l l = l l = 6.2

24 Multiplication and Division l Rule is simpler l Same number of sig figs in the answer as the least in the question l 3.6 x 653 l l 3.6 has 2 s.f. 653 has 3 s.f. l answer can only have 2 s.f. l 2400

25 Multiplication and Division l Same rules for division l 4.5 / l = 0.72 l 4.5 x l = 28 l / 1983 l =

26 Scientific Notation l Means to express a number in it’s relation to 10’s l Example: 8 x 10 2 l Rule: Pos exponent = number bigger than zero Neg exponent = number smaller than zero

27 …Scientific Notation l 8 x 10 2 Steps: l Place a decimal behind the 8 l Pos or Neg? Move the decimal the number of the exponent in the correct direction, add the zeros 8 =8 0 0= =

28 Scientific Notation l Without a calculator

29 Sci. Not. – Multiplying and Dividing l With exponents: l Multiply the bases, then add the exponents l Divide the bases, then subtract the exponents l All answers MUST be in scientific notation

30 l (2x10 3 ) x (4 x 10 5 ) –2 x 4 = 8 –3 + 5 = 8 –8 x 10 8 l (4x10 3 ) / (2 x 10 5 ) –4/2 =2 –3-5= -2 –2 x 10 -2

31 What if the answer isn’t in Sci. Notation? l (4x10 3 ) x (4 x 10 5 ) –4 x 4 = 16 –3 + 5 = 8 –16 x 10 8 l You must turn it into Sci. Notation –If you move the decimal to the right, subtract an exponent –If you move the decimal to the left, add an exponent l 1.6 x 10 9

32 Sci. Not- Sub and Adding l A little more work: –When adding decimals, the places must be lined up –Therefore, you cannot add two numbers who have different exponents l (2 x 10 2 ) + (5 x 10 3 ) = 7 x 10 5 l

33 l You must change one exponent into the other l (2 x 10 2 ) + (5 x 10 3 ) l Normal exponent rules apply (If you move the decimal to the right, subtract an exponent; If you move the decimal to the left, add an exponent) l Make sure your answer is in Sci. Not. when you are finished

34 Measuring l The numbers are only half of a measurement l It is 10 long l 10 what. l Numbers without units are meaningless. l How many feet in a yard l A mile l A rod

35 The Metric System l AKA: SI system- International System of Units l Easier to use because it is a decimal system l Every conversion is by some power of 10. l A metric unit has two parts l A prefix and a base unit. l prefix tells you how many times to divide or multiply by 10.

36 Base Units l Length - meter - m l Mass - grams - g l Time - second - s l Energy - Joules- J l Volume - Liter - L l Amount of substance - mole – mol l Temperature - Kelvin or ºCelsius K or C

37 Prefixes l Kilo K 1000 times l Hecto H 100 times l Deka D 10 times l deci d 1/10 l centi c 1/100 l milli m 1/1000 l kilometer - about 0.6 miles l centimeter - less than half an inch l millimeter - the width of a paper clip wire

38 The Metric System l King Henry Died Drinking Chocolate Milk l KHD base dcm

39 Other Prefixes l Signify the powers of 10

40 Converting khDdcm l how far you have to move on this chart, tells you how far, and which direction to move the decimal place. l The box is the base unit, meters, Liters, grams, etc.

41 Conversions l Change 5.6 m to millimeters khDdcm l starts at the base unit and move three to the right. l move the decimal point three to the right 5600

42 Dimensional Analysis l This is a structured way of helping you to convert units, and solve problems. l With this method, you can easily and automatically convert very complex units if you have the conversion formulas.

43 Using Conversion Factors l Make a fraction of the conversion formula, to convert units. l For a unit to cancel it must appear on the top and the bottom of your dimensional analysis problem.

44 Steps for Conversion Factors 1. Rewrite the problem 2. What’s on top, goes on the bottom (as far as labels go…) 3. What are you going to? 4. Which is bigger? The bigger unit gets a 1, then fill in the rest of the numbers 5. Cancel like labels (if one’s on top and the other’s on the bottom) 6. Check your labels to make sure you’re finished 7. Do the math- Top: Multiply, Bottom: Divide

45 How To Use a Metric Ruler l Contains centimeters and millimeters only. l The larger lines with numbers are centimeters, and the smallest lines are millimeters. Since millimeters are 1/10th of a centimeter, if you measure 7 marks after a centimeter, it is 1.7 centimeters long.

46 How to Use an English Ruler l More difficult to read because they deal with fractions l All rulers are marked with different markings l Link Link l Most are marked in 16ths. l Every mark is 1/16th of an inch.

47 l The center mark between numbers is 1/2. l The red lines on these rulers are marked at 1/2, and 1. l The next smallest marks on a ruler are 1/4ths. l The red marks on these rulers are at 1/4, 1/2, 3/4, and 1. (1/2 is the same as 2/4) l The next smallest marks on a ruler are 1/8ths. l The red marks on these rulers are at 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, and 1. l The next smallest mark, if there are any, are 1/16ths. l The red marks on this ruler are at 1/16, 1/8, 3/16, 1/4, 5/16, 3/8, 7/16, 1/2, 9/16, 5/8, 11/16, 3/4, 13/16, 7/8, 15/16, and 1.

48 Let’s Try It with the Smartboard!

49 Density l how heavy something is for its size l the ratio of mass to volume for a substance l D = M / V l Independent of how much of it you have l gold - high density l air low density.

50 Calculating l The formula tells you how l units will be g/mL or g/cm 3 l A sample of an unknown liquid has a mass of 11.2 g and a volume of 23 mL what is the density? l 11.2 / 23 = 0.49 g / ml

51 Density Practice l A piece of wood has a density of 0.93 g/mL and a volume of 23 cm 3 what is the mass? l 0.93 = mass / 23 cm 3 l 21 grams

52 Floating l Lower density floats on higher density. l Ice is less dense than water. l Most wood is less dense than water l Helium is less dense than air. l Water has a density of 1 g/ml l A ship is less dense than water