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

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.

Objectives1. Convert quantities and rates, including

density problems, using a dimensional analysis method.

2. Understand and express measurements and quantities using significant figures.

HOMEWORK1.5 Homework – Daily Quiz 1.6 Next Class

Agenda

1. Daily Quiz 1-52. Significant Figures3. Kahoot4. 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)

https://www.youtube.com/watch?v=2vK8iJgISXY

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 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”

https://www.youtube.com/watch?v=BhuoylQjGbU

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. 126.4 ± 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) 342.013 g b) 804.539 g

c) 20.652 g d) 49.917 g

b) Rounding if your last digit IS a 5Round these measurements. The balance is ± 0.01 g.

a) 35.055 g b) 27.665 g

c) 81.345 g d) 96.435 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 + 0.01 g. Write the numbers that should be recorded as data with the correct number of significant figures. Some answers may already be correct.

445.81 g _______________ 6.731 g _______________

5872.30 g ______________ 5.556 g _______________

5.555 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 Zeroes1 – 9 are always significant figures.

Constants (becausethey’re calculated, not measured) have an infinite number of sig figs.

The significand in an exponential number contains the sig figs.

Ex. 3.45 x 103 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. 10.01 g 140 g

0.0010 g 140.0 g 1.100 g 1100 g

140 g vs. 140.0 gWhether 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 + 3.106 g + 0.8 g (from a balance that weighs to + 0.1 g)

 9.002 m - 3.10 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)(5.1261 m) = 5.79251786 m2 = 5.79 m2

Sig figs: 3 5 (so use 3 sig figs in answer)

4.96001 g 4.740 cm3 = 1.0464135 g/cm3 = 1.046 g/cm3

Sig figs: 6 4 (so use 4 sig figs in answer)

1.5 Calculations using Significant FiguresDimensional 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 2573842 cm to three significant figures.

Example: Round 0.00302300 to three significant figures.

Significant Figures Practice (pgs. 19-20)

Mix Pair ShareWork on all the Significant

Figures Practice problems on pgs. 19-20. After time is up, we will Mix Pair Share and compare answers with a random partner

Song break!https://www.youtube.com/watch?v=ZuVPkBb-z2I

Significant Figures Kahoot

Open a web browser on your phone and go to

kahoot.itThe 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.