Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?)

Transcription

1 Obj: Students will: 1. Distinguish between accuracy and precision. 2. Examine various pieces of lab equipment for their accuracy. 3. Define and identify significant figures. Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?)

2 First a little story:

3

4 But why are you telling us all of this Mr Redden?

5 N W A handheld GPS unit is said to be accurate to about 10 feet. If you are standing within 10 ft of a box like this - it shouldn t be that hard to find.

6 But it isn t so much about the box. LOGAN FALLS

7 But if the person s GPS receiver was off by 10 ft at the time they hid it, and my GPS receiver is off by 10 ft at the time that I am trying to find it - imagine trying to find one of these on

8 But if the person s GPS receiver was off by 10 ft at the time they hid it, and my GPS receiver is off by 10 ft at the time that I am trying to find it - imagine trying to find one of these on Accuracy becomes very important!

9 But if the person s GPS receiver was off by 10 ft at the time they hid it, and my GPS receiver is off by 10 ft at the time that I am trying to find it - imagine trying to find one of these on But not only accuracy but precision as well.

10 Some definitions: Accuracy -> the condition or quality of being true, correct, or exact.

11 Some definitions: Accuracy -> the condition or quality of being true, correct, or exact. Precision -> the ability of a measurement to be consistently reproduced.

12 Some definitions: Accuracy -> the condition or quality of being true, correct, or exact. Precision -> the ability of a measurement to be consistently reproduced. If you think of it like target shooting it would be like these targets below. If you are trying to hit the center each time then... Low Accuracy Low Precision

13 Some definitions: Accuracy -> the condition or quality of being true, correct, or exact. Precision -> the ability of a measurement to be consistently reproduced. If you think of it like target shooting it would be like these targets below. If you are trying to hit the center each time then... Low Accuracy Low Precision Low Accuracy High Precision

14 Some definitions: Accuracy -> the condition or quality of being true, correct, or exact. Precision -> the ability of a measurement to be consistently reproduced. If you think of it like target shooting it would be like these targets below. If you are trying to hit the center each time then... Low Accuracy Low Precision Low Accuracy High Precision High Accuracy High Precision

15 But what does that mean when you are recording data? In recording your data for our class, you will want to be as Accurate as possible. 30 ml How would you read the graduated cylinder to the left? 20 ml

16 But what does that mean when you are recording data? In recording your data for our class, you will want to be as Accurate as possible. 30 ml How would you read the graduated cylinder to the left? You should have said 27 ml. 20 ml Accuracy describes the nearness of a measurement to the standard or true value.

17 And what about Precision? In recording your data for our class, you will want to be as precise as possible. 30 ml 30 ml 30 ml How would you read these graduated cylinders? 20 ml 20 ml 20 ml

18 And what about Precision? In recording your data for our class, you will want to be as precise as possible. 30 ml 30 ml 30 ml How would you read these graduated cylinders? 20 ml 20 ml 20 ml 26.2 ml 26.4 ml 26.5 ml Precision is the degree to which several measurements provide answers very close to each other.

19 Today s Assignment: In groups of three (3) fill in the following chart for each of the pieces of lab equipment provided. Piece of Equipment Units Smallest Graduation Can Be used to Measure to the Nearest This should be completed in your notebook.

20 Definition: - The significant figures in a number are those digits that carry meaning contributing to its precision.

21 Definition: - The significant figures in a number are those digits that carry meaning contributing to its precision. * But it can also be described as all of the numbers in a measurement plus one more for uncertainty/estimations.

22 Definition: - The significant figures in a number are those digits that carry meaning contributing to its precision. * But it can also be described as all of the numbers in a measurement plus one more for uncertainty/estimations. For example: a mass of 30.2 g indicates that it was measured to the nearest tenth of a gram while a mass of g indicates an accuracy to the nearest hundredth of a gram. So 30.2 g has three (3) sig. figs while g has four (4) sig. figs.

23 Definition: - The significant figures in a number are those digits that carry meaning contributing to its precision. * But it can also be described as all of the numbers in a measurement plus one more for uncertainty/estimations. For example: a mass of 30.2 g indicates that it was measured to the nearest tenth of a gram while a mass of g indicates an accuracy to the nearest hundredth of a gram. So 30.2 g has three (3) sig. figs while g has four (4) sig. figs. A significant figure is one which is known to be fairly reliable, it has been measured.

24 Often during this unit you will be asked how many significant figures (sig figs) a quantity has. SO there are rules concerning various digits and when they are considered significant.

25 Often during this unit you will be asked how many significant figures (sig figs) a quantity has. SO there are rules concerning various digits and when they are considered significant. Example: mg has 5 significant figures.

26 Often during this unit you will be asked how many significant figures (sig figs) a quantity has. SO there are rules concerning various digits and when they are considered significant. Example: mg has 5 significant figures. Rules for Significant Figures

27 Often during this unit you will be asked how many significant figures (sig figs) a quantity has. SO there are rules concerning various digits and when they are considered significant. Example: mg has 5 significant figures. Rules for Significant Figures ALL nonzero numbers are ALWAYS significant!!

28 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g

29 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m

30 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m In this case the quantity has been measured to the hundredths place.

31 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m A Zero is not considered significant when: it is at the end of a number. ex. 71,000 people

32 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m A Zero is not considered significant when: it is at the end of a number. ex. 71,000 people In this case the quantity has only been measured/counted to the thousands place.

33 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m A Zero is not considered significant when: it is at the end of a number. ex. 71,000 people it appears at the beginning of a number. ex L

34 Rules for Zeroes A Zero is considered significant when: it appears between two numbers ex. 205 g it follows a number and a decimal point. ex m A Zero is not considered significant when: it is at the end of a number. ex. 71,000 people it appears at the beginning of a number. ex L These circumstances are referred to as leading and trailing zeroes.

35 Your Turn #1: Using the information we just went over - how many significant figures do each of the following quantities have? cm L km g kg m 7. 3 x 10 6 m ml mg g This should be completed in your notebook.

36 Let s step back to basic arithmetic g g g and cm x cm cm 2

37 Let s step back to basic arithmetic g g g and Right?! cm x cm cm 2

38 Let s step back to basic arithmetic g g g and Right?! cm x cm cm 2 Well not in here when it comes to significant figures.

39 Let s step back to basic arithmetic g g g and Right?! cm x cm cm 2 Well not in here when it comes to significant figures. *ALL calculations, with significant figures, must be rounded to the same number of digits as the least accurately known value.*

40 That means just because you used one of these it doesn t mean that your answer is necessarily the most accurate it can be g g g cm x cm cm 2

41 That means just because you used one of these it doesn t mean that your answer is necessarily the most accurate it can be. Calculators do NOT increase accuracy g g g cm x cm cm 2 SO...

42 That means just because you used one of these it doesn t mean that your answer is necessarily the most accurate it can be. Calculators do NOT increase accuracy g g g becomes g cm becomes x cm cm cm 2 SO...

43 Rules for Calculations involving Sig Figs These rules will work in pairs of opposite operations. For addition & subtraction: we will round the answer to the smallest number of decimal places in the problem.

44 Rules for Calculations involving Sig Figs These rules will work in pairs of opposite operations. For addition & subtraction: we will round the answer to the smallest number of decimal places in the problem g g g g g g

45 Rules for Calculations involving Sig Figs These rules will work in pairs of opposite operations. For addition & subtraction: we will round the answer to the smallest number of decimal places in the problem g g g gets rounded to g g g g gets rounded to g

46 Rules for Calculations involving Sig Figs For multiplication & division: we will round the answer to the smallest number of significant figures in the problem m x 3.23 m m g L = g/l

47 Rules for Calculations involving Sig Figs For multiplication & division: we will round the answer to the smallest number of significant figures in the problem m x 3.23 m m g L = g/l gets rounded to gets rounded to 46.0 m g/l

48 Your Turn #2: Using the information we just went over - perform the following calculations and round the answer to the appropriate number of significant answers = = = = / = = 7. ( ) ( ) = = 9. ( ) + ( ) = 10. ( ) ( ) = This should be completed in your notebook.