1. Measurements and Calculations
Using Scientific Measurements

2. Scientific Notation M x 10n M is a number ≥ 1, but less than 10
n is a whole number
Can only add or subtract if n is the same
Multiplication – multiply the M’s, add the n’s
Division – divide the M’s, subtract the n’s
OR, use your calculator!

3. Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
y/x = k (k is a constant)
Can be rewritten as y = kx
When the value of y increases, the value of x also increases, and vice versa

4. Direct Proportions
Straight line
Passes through origin

5. Inverse Proportions
Two quantities are inversely proportional to each other if their product is a constant
xy = k
If x increases, y decreases and vice versa.
Graph produces a curve called a hyperbola.

6. Accuracy and Precision
Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.

7. Accuracy and Precision
Precision refers to the closeness of a set of measurements of the same quantity made in the same way. Multiple measurements are precise if they are close to each other.

8. Precision of a Measuring Tool
The precision of a measuring tool is based on how fine the markings are on the tool. The finer the markings, the more precise the tool.

10. Percent Error A measure of the accuracy of a measurement
Subtract the experimental value from the accepted value, divide by the accepted value and multiply by 100

11. Percent Error
What is the percent error for a mass measurement of 17.7g given that the correct value is 21.2 g?

12. Percent Error
A volume is measured experimentally as 4.26 mL. What is the percent error, given that the correct value is 4.15 mL?

13. Error in Measurement
There’s always some uncertainty in measurement. Results can be affected by the skill of the measurer and the precision of the instrument.

14. When you use a measuring device, you can be certain of a particular number of digits based on the markings on the device.
The last digit can be estimated by where the value is between the finest markings.
To repeat: a measurement includes all digits based on the markings on the measuring device PLUS one more figure which is estimated

15. The number of digits you include for your measurement is an indication of how precise the measuring tool was.
Therefore, for clear communication with other scientists, it is important that EVERYTIME you measure anything in the lab, you MUST record the measurement with all the digits you are sure of PLUS an estimate for the last digit.

16. Significant Figures
Significant figures are all the digits in a measurement that are known for sure, plus one final digit that is somewhat uncertain, or estimated.
Significant ≠ certain

17. Significant Figures Significant figures are only used in measurements
Counting numbers or conversion factors are considered to have an infinite number of significant figures.

18. Significant Figures All nonzero numbers are significant. 36.4 595
72395

19. Significant Figures
All zeroes that come between non-zero numbers are significant
10.5
145.09
900.4
40.006

20. Significant Figures Preceding, or leading, zeroes are not significant
0.005
0.6

21. Significant Figures
Zeros at the end of a number are significant only if there is a decimal point somewhere in the number
30.0
20.
509.00
600
75000
75000.

22. Significant Figures
In scientific notation, do not consider the exponent (or factor of 10) in the number of significant figures.
1.45 x 105
3.0 x 102
9.006 x 10-3

23. Rounding
When you perform calculations with sig figs, you may have to round your answer to get the correct number of sig figs.
Rules for rounding:
See table 2-6 on p. 48
Pay special attention to the rule for rounding 5’s

24. Addition or Subtraction
The answer must have the same precision as the least precise measurement being added or subtracted.
The key is to look at place value.

25. Multiplication and Division
Can’t have more sig figs than the measurement with the fewest number of sig figs.

26. Multistep Calculations
Some problems involve several steps.
Don’t round to correct number of sig figs in the middle of your calculations. Keep a few extra digits.
Round to the correct number of sig figs for the final answer.