1 Chapter 3: Measurement, Scientific Notation, Significant Figures Sections Chemistry 111

2 Topics Scientific Notation, Calculator Dimensional Analysis, Metric Prefixes, Per, Cancelling, Unit Paths Exercise #1 Recap / Go over Exercise Sig. Figs. Redo Ex #1, Fix sig. figs.

3 Scientific Notation Use Definitions Using the Calculator

4 Scientific Notation - Use Used to avoid: (or is it: ?) And:

5 Scientific Notation: Definitions We split the number into a “coefficient” and “exponent”: × Coefficient: –A number between & –May be positive or negative –Easy for sig. figs.! Exponent: –A positive or negative whole number –Corresponds to the number of decimal shifts. –Not involved with sig. figs.

6 Scientific Notation: Calculator Why talk about it? –Because you need to use the calculator correctly. –The calculator has a built-in function (EE or EXP) button that helps you enter exponential notation. If you learn it, it is easier, faster, more correct. (& required for Chem111)

7 Scientific Notation: Calculator II Find your button: or –Might require or function key. Find your “Negative” Key or Follow Table 3.1: (3.96×10 4 )(5.19 ×10 -7) EE 4 × EE +/- 7 = Notice that you don’t type ×10 ever, EE takes care of it. Do this & Master it today: –There are ways to do it w/o the EE button but I’ve got tricky problems to trip you up. EE EXP 2 nd Shift (-) +/ EE 4x5.197= +/- EE

8 Scientific Notation: Calculator III Try the ones in the book on page 51.

9 Dimensional Analysis Scientific Measurements –Include the numerical value:62.4 –Must also include the units: mi/hr –Number is written so it indicates how carefully it was measured (3 s.f.) but let’s put this off until later.

10 Dimensional Analysis (2) Converting between Units –How fast is a Canadian going if his speedometer says 62.4? –How far does he move every 1 second?

11 Chapter 3 - Exercise #1 1.How many  m are there in 2 miles? a.miles  km  m   m b.miles  ft  in  cm  m   m 2.The volume of a spherical Styrofoam ball with a diameter of 40 mm is calculated by V=4/3×  ×r 3 a.What is the volume? What are its units? b.What is the volume in mL? c.Draw a unit path from (b) to quarts. d.What is the volume in Quarts? e.What is the volume of 5 spherical balls in quarts? Sig. Figs.: Ignore sig. figs. as you do this exercise – make it as ugly as you can! Show your work:Write it out as if you’re teaching it to someone.!

12 Counting Significant Figures 1.Nonzero Integers. Nonzero integers always count as significant figures. 2.Zeros. There are three classes of zeros: 1.Leading Zeros are zeros that precede all the nonzero digits. These do not count as significant figures. In the number , the three zeros simply indicate the position of the decimal point. This number has only two significant figures. 2.Captive Zeros are zeros between nonzero digits, these always count as significant figures. The number has four significant figures. 3.Trailing Zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point.

13 Counting Significant Figures Note 1:In Scientific notation, all digits in the coefficient are significant figures. Note 2:Exact numbers can be considered to have a  (infinite) number of significant figures.

14 Rules for Computations & Sig. Figs. 1.For multiplication and division, the number of significant figures in the result is the same as the number with the least precise measurement used in the calculation. For example: × 4.1 =  24 2.For addition and subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation. Set the problem up like 2 nd grade math!  28.4

15 Rules for Computations & Sig. Figs. Note 1:For multiplication and division – the sig. figures are counted. Note 2:For addition and subtraction – the decimal places are counted.

16 Chapter 3 - Exercise #2 On a new Sheet of paper: –Redo the problems in Exercise #1 –Follow the sig. fig. rules. –Show the work again. Remember that some numbers came from definitions –1 inch  2.54 cm, exactly –Whole numbers –These have infinite sig. figs. – ignore them when applying sig. fig. rules.