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Wednesday, Oct. 3rd: “A” DayThursday, Oct. 4th: “B” Day

Agenda“Physical and Chemical Change” lab

Questions/CollectBegin Section 2.3: “Measurements and

Calculations in Chemistry”Anticipation GuideAccuracy, Precision, Significant Figures

Homework: Significant Figure Worksheet

Lab: “Physical and Chemical Change” Questions/Problems?

Make sure your conclusion questions are answered fully in complete sentences…

Make sure your table of contents is updated.

Sec. 2.3Anticipation Guide

Complete the anticipation guide to the best of your ability before we begin section 2.3.

Any you get correct will by X-credit!

Accuracy and PrecisionNo value that is obtained from an experiment

is exact because all measurements are subject to limits and errors.

Human errors, method errors, and the limits of the instrument are a few examples.

To reduce the impact of error on their work, scientists always repeat their measurements and calculations a number of times.

Measurements Must Involve the Right Equipment

Selecting the right piece of equipment to make your measurement is the first step to cutting down on errors in experimental results.

Accuracy is How Close a Measurement is to the True Value

Accuracy: a description of how close a measurement is to the true value of the quantity measured.

“How close am I to the bulls eye?”

Precision is How Closely Several Measurements Agree

Precision: the exactness of a measurement

How close together are several measurements of the same quantity that are measured the same way?

Accuracy and Precision

High Accuracy Low Accuracy Low AccuracyHigh Precision High Precision Low Precision

Significant Figures (Sig Figs)Significant Figure: a prescribed decimal place

that determines the amount of rounding off to be done based on the precision of the measurement.

Sig figs consist of all digits known with certainty as well as one estimated digit.

The last digit or sig fig reported after a measurement is estimated.

In the penny lab, the volume of water was recorded to the tenths place, which was an estimated digit since the graduated cylinder only had markings every 1 mL.

Rules for Determining Sig Figs1. Non-zero digits are ALWAYS significant.2. Zeros between non-zero digits are significant.3. Zeros in front of non-zero digits are NOT

significant. (They are just placeholders)4. Zeros both at the end of a number and to the

right of a decimal point ARE significant.5. Zeros both at the end of a number but to the

left of a decimal point may not be significant. If a zero has not been measured or estimated, it is not significant. A decimal placed after zeros indicates that the zeros are significant.

Sig Fig ExamplesHow many sig figs are in the following examples?12.34 grams

4 sig figs1.0053 liters

5 sig figs0.000953 meters

3 sig figs5.00

3 sig figs

More Sig Fig ExamplesHow many sig figs are in the following examples?218 kPa

3 sig figs0.025 L

2 sig figs200. m2

3 sig figs1.05 g

3 sig figs

How Do I Use Sig Figs to Round?Round each to 3 significant figures:32.068 km

32.1 km155.8 g

156 g0.02274 cm

0.0227 cm(the zero before the 2 is not significant)

Rules for Using Sig Figs in Calculations In multiplication and division problems, the

answer can’t have more sig figs than there are in the measurement with the least # of sig figs.

In addition and subtraction problems, the answer can’t have more digits to the right of the decimal point than there are in the measurement with the least # of digits to the right of the decimal.

If a calculation has both addition/subtraction and multiplication/division, round after each operation.

Calculators DO NOT Identify Sig FigsCalculate the density of isopropyl alcohol, which

has a volume of 32.4 mL and a mass of 25.42 g. Does your calculator show 0.7845679012?How many sig figs does the mass have?

4How many sig figs does the volume have?

3Since this is a division problem, the answer can’t

have more sig figs than there are in the measurement with the least # of sig figs.

The answer must be rounded to 3 sig figs, or 0.785 g/mL.

Sig Figs in a NutshellBasically, your answer CAN’T have more sig

figs than your LEAST precise measurement has!

Sig Fig Example #1Calculate the following and show the answer with

the correct number of sig figs:0.1273 mL – 0.000008 mL =

0.127292 mLThis is a subtraction problem, so the answer

should be rounded to have the same # of digits to the right of the decimal place as the value with the least # of digits to the right of the decimal.

This should be rounded to 0.1273 mL (4 digits to right of decimal point)

Sig Fig Example #2Calculate the following and show the answers with

the correct number of sig figs:(12.4 cm X 7.943 cm) + 0.0064 cm2

(Perform each operation separately/round after each)

12.4 cm X 7.943 cm = 98.4932 cm2

Round to 3 sig figs: 98.5 cm2

98.5 cm2 + 0.0064 cm2 = 98.5064 cm2

Round to 1 digit after decimal: 98.5 cm2

Example Problem A, Pg. 59A student heats 23.62 g of a solid and observes that

its temperature increases from 21.6˚C to 36.79˚C. Calculate the temperature increase per gram of solid. (Hint: round after each operation)

Temperature increase = 36.79˚C – 21.6˚C = 15.19˚C

This is rounded to 15.2˚C (1 digit after decimal)Temp change/gram of solid= 15.2˚C

23.62 g= 0.643522439 ˚C/g

This is rounded to 0.644 ˚C/g (3 sig figs)

Exact Values Have Unlimited Sig Figs

Some values that you will use in your calculations have no uncertainty.

These values have an unlimited number of sig figs and are exact values.

Examples of exact values are: Count valuesConversion factors

HomeworkSig Fig/Rounding Worksheet

You MAY work with a partner if you’d like…

Next Time:More Sig Fig Fun!