measurement unit unit description: in this unit we will focus on the mathematical tools we use in...

Measurement UnitUnit Description:• In this unit we will focus on the

mathematical tools we use in science, especially chemistry – the metric system and moles.

• We will also talk about how to gauge the accuracy and precision of our measurements.

Measurement UnitThe Big Questions• How do we measure things in chemistry?• Why are units so important?• How accurate and precise are my

measurements and how can I show this in my calculations?

• How can I move between different measurement units?

• What the heck are moles and why are they important?

Measurement UnitReview Topics:• scientific notation and exponents• metric system• algebra• density calculations• dimensional analysis – conversions• temperature conversions

Measurement UnitNew Topics:• rounding in chemistry – significant

figures• determining uncertainty of a

measurement• % error• accuracy vs. precision

Measurement UnitNew Topics:

Moles!

and related topics…

Accuracy and Precision• Accuracy = how close one comes to the

actual value (absolute error)

• Precision = the agreement of two or more measurements that have been made in the same way (reproducibility)

Accuracy and PrecisionCan you have accuracy without precision?

Or precision without accuracy?

Why or why not?

What are significant figures and why do we use them?

• Measurements are dependent on the instruments we use.

• We round our measurements to reflect the level of precision of these instruments.

• These are significant figures.

Rules for Recognizing Significant Figures

1. Non-zero numbers are always significant.

2. Zeros between non-zero numbers are always significant.

3. All final zeros to the right of the decimal place (i.e. after digits) are significant.

Rules for Recognizing Significant Figures

4. Zeros that act as placeholders are not significant.

Convert quantities to scientific notation to remove the placeholder zeros.

5. Counting numbers and defined constants have an infinite/unlimited number of significant figures.

How many sig figs are in the following measurements?

1. 46 g 7. 0.04066 g

2. 406 g 8. 0.00406600 g

3. 460 g 9. 1.04066 g

4. 460. g 10. 100.040660 g

5. 460.0 g 11. 1000466 g

6. 40660 g 12. 100046600 g

How many sig figs are in the following measurements?

1. 46 g 2 7. 0.04066 g 4

2. 406 g 3 8. 0.00406600 g 6

3. 460 g 2 9. 1.04066 g 6

4. 460. g 3 10. 100.040660 g 9

5. 460.0 g 4 11. 1000466 g 7

6. 40660 g 4 12. 100046600 g 7

Rules for Rounding NumbersIf the digit to the immediate right of the last significant figure is

1. < 5, do not change the last significant figure.

2. > 5, round up the last significant figure.

Rules for Rounding NumbersIf the digit to the immediate right of the last significant figure is

3. = 5, and is followed by a nonzero digit, round up the last significant figure.

4. = 5, and is not followed by a non-zero digit, look at the last significant figure.If it is an odd digit, round it up. If it is an even digit, do not round up.

Rounding Practice: Round the following measurements to two sig figs:13.4 g13.5 g13.51 g14.5 g14.51 g14.500001 g14.500000 g10.5 g

Rounding Practice: Round the following measurements to two sig figs:13.4 g 13 g13.5 g 14 g13.51 g 14 g14.5 g 14 g14.51 g 15 g14.500001 g 15 g14.500000 g 14 g10.5 g 10. g

Significant Figures in Measurement

consist of all parts of the measurement that you know for sure

+ one estimated digit

e.g. metric ruler, thermometer

Significant FiguresWhat about electronic instruments?

e.g. electronic balances, digital thermometers

The electronics within the instrument estimate the last digit.

Addition and SubtractionYou cannot be more precise than your last uncertain number. If the mass of something weighed on a truck scale was added to the mass of an object weighed on one of our centigram balances, the sum would NOT be precise to 0.01 g.

Addition and SubtractionIf you circle the uncertain number (which is significant), it can be seen that in additions and subtractions, you round off to the left-most uncertain number.

Addition and Subtractione.g. 20.53

6.6 3.98631.116 31.1

An answer is reported to ONE uncertain number.Therefore 31.116 is rounded off to 31.1.

Multiplication and Division• The product or quotient is precise to the number

of significant figures contained in the least precise factor.

e.g. 1: 63.2 cm x 5.1 cm = 322.3 cm2 320 cm2 (2 sfs)e.g. 2: 5.30 m x 0.006 m = 0.0318 m2 0.03 m2 (1 sf)

Sig Fig Practice Addition/Subtraction and Multiplication/Division

1. Calculate and round to the correct number of sig figs.a) 4.53 x 0.01 x 700 =b) 2 x 4 x 50400 =c) _0.01_ =

0.0001d) 3211 + 0.1590 + 3.2 = e) 45119.32 – 0.001530 =

2. (8.7 + 15.43 + 19) =(4.32 x 1.7)

Sig Fig Practice Addition/Subtraction and Multiplication/Division

1. Calculate and round to the correct number of sig figs.a) 4.53 x 0.01 x 700 = 30b) 2 x 4 x 50400 = 400,000c) _0.01_ = 100

0.0001d) 3211 + 0.1590 + 3.2 = 3214e) 45119.32 – 0.001530 = 45119.32

2. (8.7 + 15.43 + 19) = 5.9(4.32 x 1.7)

More Sig Fig Practice Addition/Subtraction and Multiplication/Division

Perform each of the following mathematical operations and express each result to the correct number of significant figures.

1. 9.5 mL + 4.1 mL + 2.8 mL + 3.175 mL =4

(this is an averaging calculation)

2. (8.925 g – 8.804 g) x 100% =8.925 g

3. (9.025 g/mL – 9.024 g/mL) x 100% = 9.025 g/mL

More Sig Fig Practice Addition/Subtraction and Multiplication/Division

Perform each of the following mathematical operations and express each result to the correct number of significant figures.

1. 9.5 mL + 4.1 mL + 2.8 mL + 3.175 mL =4.90 mL4

(this is an averaging calculation)

2. (8.925 g – 8.804 g) x 100% = 1.36%8.925 g

3. (9.025 g/mL – 9.024 g/mL) x 100% = 0.01% 9.025 g/mL

More Sig Fig Practice (Honors)Addition/Subtraction and Multiplication/Division

Perform each of the following mathematical operations and express each result to the correct number of significant figures.

4. 4.184 x 100.62 x (25.27-24.16) =

5. (9.04 – 8.23 + 21.954 + 81.0) 3.1416 =

6. 8.27 (4.987 – 4.962) =

7. 1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1 =

8. (1.0086 – 1.00728) = 6.02205 x 1023

More Sig Fig Practice (Honors)Addition/Subtraction and Multiplication/Division

Perform each of the following mathematical operations and express each result to the correct number of significant figures.

4. 4.184 x 100.62 x (25.27-24.16) = 467

5. (9.04 – 8.23 + 21.954 + 81.0) 3.1416 = 33.04

6. 8.27 (4.987 – 4.962) = 0.21

7. 1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1 = 2.020 x 10-1

8. (1.0086 – 1.00728) = 2.2 x 10-27

6.02205 x 1023

Uncertainty in Measurement• The last place of a measurement is always

an estimate.

• The size of the estimate is based on the reliability of the instrument range within which the measured value probably lies

Uncertainty in Measurement• Report to only one sig fig.• That digit should be in the same decimal

place as the last sig fig of the measurement.Correct Incorrect

36.5 ± 0.5 m 36.5 ± 0.25 m

300.4 ± 0.2 g 300.4 ± 0.06 g

230 ± 10 s 232.4 ± 5 s

Uncertainty in Measurement• Report to only one sig fig.• That digit should be in the same decimal

place as the last sig fig of the measurement.Correct Incorrect

36.5 ± 0.5 m 36.5 ± 0.25 m 36.5 ± 0.2 m

300.4 ± 0.2 g 300.4 ± 0.06 g 300.4 ± 0.1 g

230 ± 10 s 232.4 ± 5 s 232 ± 5 s

Percent Error

|theoretical – actual| x 100% = ___ %theoretical

“what you should have got” – “what you got” x 100% “what you should have got”