1 Chapter 1 Scientific measurement & Significant Figures

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 Quantitative Qualitative Quantitative

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 word 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 anaolgy

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 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 mean anything 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 142 cm? l 140 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 Only measurements have sig figs. l Counted numbers are exact l A dozen is exactly 12 l A a piece of paper is measured 11 inches tall. l Being able to locate, and count significant figures is an important skill.

18 Sig figs. l How many sig figs in the following measurements? l 458 g l 4085 g l 4850 g l g l g l g

19 Sig Figs. l g l 4050 g l g l g l g l Next we learn the rules for calculations

20 More Sig Figs

21 Problems l 50 is only 1 significant figure l if it really has two, how can I write it? l A zero at the end only counts after the decimal place l Scientific notation l 5.0 x 10 1 l now the zero counts.

22 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

23 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

24 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

25 Practice l l l l 6.0 x x 10 3 l l l l 6.0 x x 10 -3

26 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

27 Multiplication and Division l Same rules for division l practice l 4.5 / l 4.5 x l x.043 l / 1983 l / 714

28 The Metric System An easy way to measure

29 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

30 The Metric System 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.

31 Base Units l Length - meter more than a yard - m l Mass - grams - a bout a raisin - g l Time - second - s l Temperature - Kelvin or ºCelsius K or C l Energy - Joules- J l Volume - Liter - half f a two liter bottle- L l Amount of substance - mole - mol

32 Prefixes l kilo k 1000 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

33 Volume l calculated by multiplying L x W x H l Liter the volume of a cube 1 dm (10 cm) on a side l so 1 L = 10 cm x 10 cm x 10 cm l 1 L = 1000 cm 3 l 1/1000 L = 1 cm 3 l 1 mL = 1 cm 3

34 Volume l 1 L about 1/4 of a gallon - a quart l 1 mL is about 20 drops of water or 1 sugar cube

35 Mass l weight is a force, is the amount of matter. l 1gram is defined as the mass of 1 cm 3 of water at 4 ºC. l 1000 g = 1000 cm 3 of water l 1 kg = 1 L of water

36 Mass l 1 kg = 2.5 lbs l 1 g = 1 paper clip l 1 mg = 10 grains of salt or 2 drops of water.

37 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.

38 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

39 Conversions l convert 25 mg to grams l convert 0.45 km to mm l convert 35 mL to liters l It works because the math works, we are dividing or multiplying by 10 the correct number of times khDdcm

40 Conversions l Change 5.6 km to millimeters khDdcm

41 Which is heavier? it depends

42 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.

43 Calculating l The formula tells you how l units will be g/mL or g/cm 3 l A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density? l A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

44 Calculating l A piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume? l The units must always work out. l Algebra 1 l Get the thing you want by itself, on the top. l What ever you do to onside, do to the other

45 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 A ship is less dense than water

46 Density of water l 1 g of water is 1 mL of water. l density of water is 1 g/mL l at 4ºC l otherwise it is less

47 Measuring Temperature l Celsius scale. l water freezes at 0ºC l water boils at 100ºC l body temperature 37ºC l room temperature ºC 0ºC

48 Measuring Temperature l Kelvin starts at absolute zero (-273 º C) l degrees are the same size l C = K -273 l K = C l Kelvin is always bigger. l Kelvin can never be negative. 273 K

49 Heat a form of energy

50 Temperature is different l than heat. l Temperature is which way heat will flow (from hot to cold) l Heat is energy, ability to do work. l A drop of boiling water hurts, l kilogram of boiling water kills

51 Units of heat are l calories or Joules l 1 calorie is the amount of heat needed to raise the temperature of 1 gram of water by 1ºC l a food Calorie is really a kilocalorie l How much energy is absorbed to heat 15 grams of water by 25ºC l 1 calorie = 4.18 J

52 Some things heat up easily l some take a great deal of energy to change their temperature. l The Specific Heat Capacity amount of heat to change the temperature of 1 g of a substance by 1ºC l specific heat SH l S.H. = heat(cal) mass(g) x change in temp(ºC)

53 Specific Heat l table page 42 l Water has a high specific heat l 1 cal/gºC l units will always be cal/gºC l or J/gºC l the amount of heat it takes to heat something is the same as the amount of heat it gives off when it cools because...

54 Problems l It takes 24.3 calories to heat 15.4 g of a metal from 22 ºC to 33ºC. What is the specific heat of the metal? l Iron has a specific heat of 0.11 cal/gºC. How much heat will it take to change the temperature of 48.3 g of iron by 32.4ºC?