Warm Up1. How many miles is 870,655 in? (Hint: There are 5,280 ft in 1 mile).

2. Do you weigh yourself? Which scale would you use? Why? How do you know how accurate you are?

2

• Determine the length of the red line.

What is the value of the lines between the 2 cm and 3 cm marks?

0.1 cmSo this line is at least 2.8 cmIs it exactly on the line?What would the imaginary lines between 0.8 and 0.9 be worth?

.01 cm

Since it is hard to estimate where it is between the lines just say it is half way if it is between the lines or .05 cm, if it is on the line, keep the decimal place but just report a zero or .00 cm.What is the length of the red line here?

2.85 cm

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Significant Figures

• The Atlantic/Pacific rule:If a decimal is absent, start on the Atlantic side of the number.

20815000

Go through all zeros until you hit a real number. All digits after that are significant.

5 significant

digits

0.00007895

If a decimal is present, start on the Pacific side of the number.Go through all

zeros until you hit a real number. All digits after that are significant.

4 significant

digits

4

25428.51

Calculations with Significant digits

Addition & Subtraction: report you answer in the least decimal places as your data.

25428.5

13.81

.0045

25413.00131.7+

This is the last digit but you must calculate the next one to see if

you should round

5

Multiplication & Division: report your answer in the least number of significant digits as your data.

45.3 x 67.9008

3 digits 6 digits

= 3075.9062 3080or

3.08 x103

You try:

6.87 + 28.1 + 570.3368 =

67.38 / 59.256 =

Scientific notation can be used to report the correct number of significant digits

Do not round your data until you are finished with all calculations.

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• This is used to make very large and very small numbers manageable. Ex. 4,763,000,000 = ?

• Report only one digit to the left of the decimal.• Multiply by a power of 10 that you have removed from

original number.• If your number becomes smaller by moving the decimal-

your exponent should be larger. Ex. 4.763 X 109 greater than 0.

• If your number becomes larger by moving the decimal- your exponent should be smaller (be careful of negative numbers).

Ex. 0.000 007 = 7 X 10-6 smaller than 0.

Scientific Notation

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Errors in data

There are numerous types of errors that can occur in the lab.

1. Equipment error: This happens when the equipment used for an experiment wasn’t calibrated or is faulty. The error tends to be consistent throughout the data. This usually results in data that is precise but not accurate.

2. Operator error: These are mistakes made by the experimenter. It may be technique problems or mistakes that result in regular errors occurring each time. These results are usually neither precise nor accurate.

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Errors in data• Errors can all average out to be an accurate

value by coincidence. This would not be precise but accurate.

• The best is to strive for both precision and accuracy to achieve the best data possible,

• The best way to gather data is to take multiple measurements (minimum of three) of the same data and then taking an average of the data.

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Calculating Percent Error• The percent error calculation is used to see how

far off your experimental data is from the theoretical, accepted, book or true value.

• An acceptable variance is within 5% of the true value.

% Error = |True value – Experimental value| x100 True value

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Dimensional analysis

1. Put the given value in your problem over 1.58.3 in. 1

2. Decide what conversion factor or equality you need to use by comparing what unit you have in the problem with the unit you are trying to change it to and write it on your paper.

• 58.3 in. = ? ft• I will use 12 inches = 1 foot

(Be sure the measurement has only one unit. You can only change one unit at a time)

58.3 in. = ? ft

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3. Write the conversion factor as a quotient (a fraction) so that the unit you are changing is canceled (on the bottom of the quotient) and the unit you want to keep is left (on the top of the quotient).

12 in. = 1 ft. 12 in. or 1 ft.

1 ft. 12 in.

58.3 in. 1 ft.

1 12 in.

4. Carry out the math to solve for the desired value being sure to follow the order of operations for math.

58.3 in. 1 ft. = 4.86

1 12 in.

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5. Finally, make sure you list the new unit with your number. If you did it right your old unit should cancel and the new unit will be left.

58.3 in. 1 ft. = 4.86 1 12 in.

ft.