Thursday 9-03 and Friday 9-04 Significant Figures Mrs. wilson

The hand signal  If I need your quiet attention, I’ll raise my hand and stop speaking.  If you raise your hand and go quiet, we can get started quicker!

Daily Quiz 1-5  Obtain a calculator and periodic table.  Work by yourself. Work silently.  Turn in your completed quiz into the Class In Bin.  Return the periodic table after the quiz.  Open your packet to section 1.5.

Objectives 1. Convert quantities and rates, including density problems, using a dimensional analysis method. 2. Understand and express measurements and quantities using significant figures. HOMEWORK 1.5 Homework – Daily Quiz 1.6 Next Class

Agenda 1. Daily Quiz Significant Figures 3. Kahoot 4. Exit Ticket

Why care about significant figures anyway?  Any measurement has a certain number of significant figures.  The number of significant figures is the number of digits believed to be correct by the person who’s measuring.  It ALWAYS includes one estimated digit – this will lie within the uncertainty limit of your measurement.  You cannot record more digits than your measuring instrument is capable of giving. Your measurements should reflect the quality of your tools.

A Real Life Example (since I knew you’d ask) iJgISXY The digital touchpad used in the race only measured to the hundredths place. What would have happened if it measured to the tenths? Or the thousandths?

What is the length of the bar on each ruler? ** Don’t forget to record one uncertain digit.

What’s the length of the bar?

“How to Use a Bathroom scale” Watch the scale readings carefully.

“how to use a bathroom scale” Think Pair Share: Answer these questions, orally, with a partner. 1. Which digit(s) in each measurement was/were“significant”? 2. What is the uncertainty of the scale measurements? How do you know?

1.5 Significant figures (pg. 15) It is important to make accurate measurements and to record them correctly so that the accuracy of the measurement is reflected in the number recorded. No physical measurement is exact; every measurement has some uncertainty. The recorded measurement should reflect that uncertainty. One way to do that is to attach an uncertainty to the recorded number. Ex ± 0.1 pounds Another way to indicate uncertainty is the use of significant figures.

1.5 Significant Figures (pg. 15) a) Rounding if your last digit is NOT a 5 Round these measurements. The uncertainty is ± 0.01 g. a) gb) g c) gd) g

b ) Rounding if your last digit IS a 5 Round these measurements. The balance is ± 0.01 g. a) g b) g c) g d) g If the doubtful digit is odd, round up. If it is even, round down. ** Why round up sometimes and down sometimes? If you always round up when the last digit is 5, this will introduce systematic error that causes all your values to be too high.

Practice: The uncertainty of a balance measurement is g. Write the numbers that should be recorded as data with the correct number of significant figures. Some answers may already be correct g _______________6.731 g _______________ g ______________5.556 g _______________ g________5.565 g ___________

1.5 Significant figures (pg. 15)  Using uncertainty all the time gets cumbersome… so alternatively we can use significant figures to express the degree of certainty in our measurements.

1.5 Significant Figures and Zeroes 1 – 9 are always significant figures. Constants (because they’re calculated, not measured) have an infinite number of sig figs. The significand in an exponential number contains the sig figs. Ex x 10 3 m has three significant figures.

Back to Michael Phelps…  … who won that race by 0.01 seconds.  If we considered placeholder zeroes to be significant (making 0.01 have two significant figures) and wanted to round to the tenths place… we’d get 0.0. No one can win a race by that margin!

Practice: Determine the correct number of significant figures in the following numbers g140 g g g g1100 g

140 g vs g Whether you get “140 g” or “140.0 g” as a reading depends entirely on the precision level of your balance. A balance that can only give you “140 g” and no more most likely has an uncertainty of ± 1 g. (Generally the very last digit tells you uncertainty.) A balance that can give you “140.0 g” as a reading most likely has an uncertainty of ± 0.1 g. This means that this balance has a greater amount of precision and thus more significant figures.

1.5 Calculations using Significant Figures In adding or subtracting numbers, the answer should contain only as many decimal places as the measurement having the least number of decimal places. Practice: 16.0 g g g (from a balance that weighs to g) m m (from a meter stick that measures to the nearest cm)

1.5 Calculations using significant figures When multiplying or dividing, the answer may have only as many significant figures as the measurement with the least number of significant figures. Examples:(1.13 m)( m)= m 2 = 5.79 m 2 Sig figs: 3 5 (so use 3 sig figs in answer) g  cm 3 = g/cm 3 = g/cm 3 Sig figs: 6 4 (so use 4 sig figs in answer)

1.5 Calculations using Significant Figures Dimensional Analysis and converting between two sets of units never changes the number of significant figures in a measurement. Convert and express the conversion with correct number of significant figures: 30.0 cm/s  in/min

Rounding to get the right number of sig figs Example: Round cm to three significant figures. Example: Round to three significant figures.

Significant Figures Practice (pgs )  Mix Pair Share  Work on all the Significant Figures Practice problems on pgs After time is up, we will Mix Pair Share and compare answers with a random partner

Song break!

Significant Figures Kahoot  Open a web browser on your phone and go to kahoot.it  The Game Pin will appear on the screen momentarily.

Exit Ticket Describe five things you learned about significant figures. End of Class Procedure: Complete and turn in your exit ticket by yourself. You may not use any notes. Put your books etc. away. Wait for dismissal. Please, no phones! Clean up your table. When you are dismissed by me (not the bell), push in your chairs straight as you leave. Homework: 1.5 Homework and Significant Figures Practice on pg. 19. Daily Quiz 1-6 next class.