Certainty in Measurement, Significant Figures, and Scientific Notation

Certainty in Measurement, Significant Figures, and Scientific Notation

Class on 9/3/2013

Scribe Post Author: Jordan C.

The quiz that we were originally supposed to take on Wednesday, the 4th was moved to Friday, the 6th. If you have any family conflicts with the holiday, make sure to contact Mrs. Friedmann.

Questions of today:

• Remember accuracy and precision? 
• Hows do they relate to lab equipment? What is certainty in measurement?
• What are significant figures? What rules go with them?
• Remember scientific notation?
• How can I do a conversion if i can't just shift the decimal? What is dimensional analysis? 

Review on the difference of precision and accuracy:

• It is possible to be precise and accurate if the correct answer is received multiple times in a very close range. Example: measuring a dog and get 11.2 pounds, 11.1 pounds, and 11.4 pounds. All these points are very close to correct and are practically same.
• It is possible to be precise but no accurate if the same but not correct answer is received multiple times in a very close range. Example: measuring a substance produced and get 11.1 mL, 11.0 mL, and 11.2 mL when the correct answer was 13 mL. 
• It is not possible to be truly accurate without being precise. The correct answer cannot be a set of a large range numbers. This holds true for measuring in a lab.
• The main idea to take with you is when measuring in a lab, you can get a false sense of accuracy  related to the equipment if your answer is precise but not accurate.

Homework check:

The homework of metic conversion practice in our composition notebooks was checked in and we later corrected our work. Please see Mrs. Friedmann if you have any questions. On #10, it is important to know that 1 cm^3 is the same thing as 1 mL (1 cm^3=1 mL).

Measures of Uncertainty:

We learned the measure of uncertainty when using lab equipment. Firstly, remember to measure from the bottom of the meniscus because the water likes to stick to the sides of the equipment.

10 mL Graduated Cylinder:

As you can see, the increments are divided into the tenths place. So, you are certain up to the tenths place because there is a mark. So you would have a certainty of measuring 8.6 and and uncertainty of 8.65 (you use uncertainty with the last digit place). If the measurement is right on the increment, you would measure 8.60 with a 0 for the uncertainty. When the unlabeled marks are 1/10 the value of the labeled marks, you are certain of them.

100 mL Graduated Cylinder:

As you can see, the increments are divided into whole numbers, so there is an uncertainty is to the tenths place. It is certain because there is a mark. When the unlabeled marks are 1/10 the value of the labeled marks, you are certain of them. You can be sure of measuring 33 and uncertain of 33.2 since there are no tenths marks as well. 

50 mL Beaker:

This equipment is divided into increments of 5. Going by: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.

You could measure 16 mL, but you would also be unsure of this because there is only marking by multiples of 5. You are certain of 16, and uncertain about 16. When the unlabeled marks are 1/2 the value of the labeled marks, ignore them--you are not certain of them. 

Significant figures:

The powerpoint to go along with these notes is in the note section of the Moodle page. 

The rules for counting significant figures:

• Nonzero integers (positive whole numbers other than 0) always count as significant figures (3456 has 4 significant figures). 
• Leading zeros are never significant (0.000072 only has 2 significant figures)
• Captive zeros (0 in-between nonzero integers) always count as significant figures. (12.07 has 4 significant figures)
• Trailing zeros are significant only if the number contains a decimal point (9.300 has 4 significant figures, 10 has 1 significant figure 10. has 2 significant figures)

Mathematical operations and Significant figures:

Adding and Subtracting:
Number of significant figures in the result, after adding or subtracting, equals the number of decimal places in the least precise measurement (number of decimal places is the same as the greatest uncertainty). You add of subtract normally and then you use the number that has the least amount of decimal places into the answer. (6.8 + 11.934 = 18.734, then it turns into 18.7 because the number 6.8 also has only one decimal place. 

Multiplying and Dividing:
The number of significant figures in the result equals the number in the least precise measurement (least amount of significant figures) used in the calculation. (6.38*2.0=12.76, then it turns into 13 because 2.0 only has 2 significant figures--the least amount of significant figures in the calculation)

Exact numbers and significant figures

If a mathematical operations, certain numbers involved in calculations are exact and do not affect the number of the significant figure to be reported. Exact numbers like (tempF=1.8(tempC) +32. The bolded numbers do not limit the number of significant figures in this equation). 

Scientific notation

This allows easy conversion from decimal from to powers of 10. To set up scientific notation, the number has to be only one number before the decimal (like 3.456 or 5.97979797) when it is raised to a power of 10. The number after the 10 tells you how many spaces to move the decimal to the left or right. The number in the scientific notation (5.456*10^3) tells you how many significant figures there are (4 in the example). 

Homework

1) Finish the blue practice sheet ("Unit Conversions, Dimensional Analysis...etc.") handed out in class today (in the Unit 1 Handouts folder).  Due Friday.

2) WebAssign 1.2 -- Units, Conversions, and Scientific Notation -- due tonight, 11:59 pm. 

3) There will be a quiz on Friday, mainly on the material we practiced in class today, although anything we have learned so far is fair game!  

**Please email me BEFORE FRIDAY if you foresee any difficulty getting your homework done due to Rosh Hashanah obligations, including preparing for the quiz.** 

Remember the quiz has been moved to Friday, the 6th.

The next scribe author will be: Ashley M.