Davis. 1.Measurements 2.Understand Uncertainty in Measurement 3.Know, understand, and be able to...

Chemistry 139

Davis

Chapter 1 – Goals

Chapter 2 - Goals

1. Measurements2. Understand Uncertainty in Measurement3. Know, understand, and be able to apply

significant figures to calculations.4. Know, understand, and be able to apply

scientific notation to calculations.

Measurement…

Defined: determination of the quantities related to an object.

Dimensions Volumes TimeEtc…

Requires that someone actually

I’m certainly uncertain…Two terms:1. Exact numbers – • Exactly • Exactly • Exactly _____ desks in this room.

2. Inexact numbers –

•Flaws in •Uncalibrated•User

Accuracy and Precision

DefinedPrecision –

Accuracy –

Volume measurements for a titration:

Trial 1 = 25.5 mLTrial 2 = 25.6 mLTrial 3 = 25.5 mL

Is this accurate or precise or…?

Sample data

Mass readings for a magnesium sample:

Trial 1 Trial 2 Trial 30.155 g 0.157 g 0.135 g

Evaluate these measurements for precision and accuracy

From the book:

Two teams of three students count birds sitting on a power line. Team counts are:

Team A Team BMarjorie: 71 Howard: 76Marlene: 74 Alice: 76Kathleen: 71 Sharon: 67

Who was most accurate?Which team was most accurate?Which team’s count was most precise?

The actual count was 76 birds.

Uncertainty in MeasurementWhy are digits in measurements uncertain?

1. Instruments • • Differences

2. Always involves estimation Choose the right instrument for the job

Volumetric vs ‘to hold’ glassware May be estimated for you (electronic

scales) Scale is marked but you estimate the in-

between

Glassware/proper equipment

Measurements

MUST

Which is correct?

Significant Figures (Digits)…

Method to deal with All digits known

What Sig Figs mean…

All KNOWN numbers

15023.557

Significant DigitsThe Rules – Memorize these.All non-zeros are A zero is significant when :

It is It is

A zero is not significant when:It is It is at

Significant Digits - PRACTICE

How many significant digits?1. 54.232. 23.000053. 0.00044. 350005. 0.0005046. 45.6232007. 5,000,0008. 4,000,000.1

Calculations with Significant Figures

Add/subtract –

Multiply/divide –

Only round after problem is complete

Practice Add/Subtract

122.53 + 6.448 + 145.3 274.278

Significant Digits - Calculations

Addition and SubtractionRound answer to have final digit in the SAME PLACE as the last digit in the LEAST ACCURATE MEASUREMENT

1.21 + 5.002 + 10. = 34.5 + 12.45 + 23.0505 = 186.31 + 11.1 = 12.0231 + 3.86 = 0.100012 + 120. = 1200 + 12 + 15 + 0.5 =

Significant Digits - Calculations

Multiplication and DivisionThe answer has as many sig figs as the number with the fewest sig figs

14.8 x 3.1 = 18.2 x 3.0 =52/1.5 =321.868783 x 1 =2400 x 2.123 =15000/12.354 =

Practice Multiply/Divde

452.11 x 78.5 = 35490.635

Practice

1524.57 / 32.15 = 47.4205287714

Significant Figures and Exact Numbers

Exact numbers are never used to determine the number of significant figures to report in your answer.

6.25 ft * 1 mile 5280 ft

= 0.00118371212 mile

Scientific Notation

Convenient way of writing very large or very small numbers and showing only significant figuresNumber between 5120 becomes Move decimal point in original number to make number 1-10Move left = Move right =

Scientific Notation Practice

123,000 =0.000045 =23.45 =0.0000000003 =1,000,000 =

Scientific Notation and Significant Figures

Express the number 275,364,145 with:

4 sig fig:

2 sig fig:

6 sig fig:

Scientific Notation

Math with:Use the EE or EXP button on your calculator.For example: