Tuesday September 15, 2009 Objectives: SWBAT distinguish between precision and accuracy. SWBAT represent numbers in scientific notation. SWBAT calculate the number of significant figures SWBAT use dimensional analysis to solve mathematical problems.

Warm Up 9/15/2009 The earth is 2.38 X 10^5 miles from the moon. How far is that? How far is that in kilometer if 1 mile = 1.6 km? How many seconds ARE in one day? How could I write 4,560,000 in scientific notation? What does 3.5X10^-6 mean?

Our Unit Measurements Mass Volume Length Definition Units Used The measure of the amount of matter The space occupied by the object Measure of a dimension Units Used Kg L, ml or cm^3 Km, m, cm Tool Used Balance Graduated cylinder or meter stick Meter stick Method LWH or displacement

Volume by Displacement Meniscus meniscus

Calculating Volume Volume = LWH What’s the volume of this box? How many decimal places should we go to?

Are you accurate or precise? Accuracy: how close are you to the correct value? Precision: How close are you to a value each time? Error: experimental value – accepted value Percent error: IerrorI accepted value X 100%

Calculate %error How far are you from the intended value? How close are you? Example: You record a temperature of 90C° but the correct value for the boiling point of water is 100C°. What is your percent error?

Do Decimal Places Matter? Easy Answer, they are significant! Measurements must ALWAYS be reported to the correct number of sig. figs, it’s a matter of precision.

Which digits are significant? Every non-zero digit. ex. 24.7m , 0.743m, and 714m 2. Zeroes between nonzero digits. ex. 7003m , 40.79m, and 1.503m 3. Leftmost zeros are not. ex. 0.0071m, 0.42m, and 0.000099m

More Rules for Sig Figs 4. Zeros at right of decimal and at end of number are. ex. 43.00m, 1.010m, and 9.000m 5. Zeros to the right at the end before the decimal are not. ex. 300m, 7000, and 27,210m 6. All digits written in scientific notation are significant.

Adding/Subtracting Mult/Div Significant Figures Addition and Subtraction Rule: Decimal places should be rounded to same number of decimal places as the measurement with the least number of decimal places. Multiplication and Division Rule: Round to the answer to the same number of sig. figs. as the measurement with the least number of sig. figs.

Last But not Least: Scientific Notation There must be a non-zero-digit to the left of the decimal. The exponent on the tens should represent the number of “tens” skipped. Ex. 6,300,000 = 6.3 X 10^6 (to the left (+)) 0.000008 = 8 X 10^-6 (to the right (-)) *digits must be in significant figures!

Homework R58: #1-5 R61: #1-5 Do this in homework section. Do only a,b for each.