1. Scientific Measurement And Dimensional Analysis
Chapter 3 & 4

2. Measurement Qualitative Measurements:
Give results in descriptive, nonnumeric form
Example: The baby feels hot
Quantitative Measurements:
Give results in definite form as units and numbers
Example: 273 K

3. Scientific Notation A number written as the product of two numbers
A coeffficient and 10 raised to a power
Numbers larger than 1 have positive exponents
Numbers less than 1 have negative exponents
Move your decimal between the first and second digits.
Example: 36,000 = 3.6 x 104
Example: = 3.6 x 10-4

4. Break it down
3.6 x 104 = 3.6 x 10 x 10 x 10 x 10
= 36, 000!
3.6 x 10-4 =
10x10x10x10
= !

5. Try some!
1,100 =
250,000 =
68,000,000 =
250 =
.000,000,56 =
.003,4 =
.000,000,001,1 =

6. Answers
1,100 = 1.1 x 103
250,000 = 2.5 x 105
68,000,000 = 6.8 x 107
250 = 2.5 x 102
.000,000,56 = 5.6 x 10-7
.003,4 = 3.4 x 10-3
.000,000,001,1 =1.1 x 10-9

7. ROUNDING >5  round previous digit up one
What if the digit to be dropped is:
>5  round previous digit up one
<5  do not change previous digit

8. Multiplication Division
Multiply numbers then add the exponents
Example: (2.0 x 102) (2.0 x 105)
2.0 x 2.0 = 4.0
= 107
 Answer =
4.0 x 107

9. Division Divide numbers then subtract the exponents.
Example: 5.0 x 10-10
2.5 x 10-2
5.0/2.5 = 2.0
(-10 – (-2) ) = = -8
 Answer =
2.0 x 10-8

10. Try some! (3.0 x 103)(2.0 x 10-5) = (2.5 x 10-2)(3.0 x 10-8) =

11. Answers
(3.0 x 103)(2.0 x 10-5) = 6.0 x 10-2
(2.5 x 10-2)(3.0 x 10-8) = 7.5 x 10-10
(5.0 x 10-10)(2.0 x 100) = 10. x 10-10
(2.0 x 10-2)/(1.0 x 10-4) = 2.0 x 102
(8.0 x 105)/(4.0 x 10-10) = 2.0 x 1015
(5.0 x 10-1)/(1.0 x 10-1) = 5.0 x 100

12. Addition & Subtraction
Exponents must be the same
Fix them if different
Example:
5.40 x 103
x or .600 x 101)102 = 103
Move your decimal + or - and increase or decrease your exponent. Then add!

13. Addition & Subtraction
5.40 x 103
x 103
6.00 x 103
8.00 x 104
x 105 20.0 x 10-1)105 = 104
= 12.0 x 104 (not in scientific notation)
= 1.20 x 105

14. Try Some!
(4.0 x 10-10) + (2.0 x 10-9) =
(5.0 x 10-2) + ( 6.0 x 10-2) =
(1.0 x 102) – (5.0 x 101) =
(6.0 x 10-3) – (6.0 x 10-2) =
(10. x 101) + (9.0 x 101) =

15. Answers!
(4.0 x 10-10) + (2.0 x 10-9) = 2.4 x 10-9
(5.0 x 10-2) + ( 6.0 x 10-2) = 1.1 x 10-1
(1.0 x 102) – (5.0 x 101) = 5 x 101
(6.0 x 10-3) – (6.0 x 10-2) = 5.4 x 10-2
(10. x 101) + (9.0 x 101) = 1.9 x 102

16. Accuracy vs. Precision
Even the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments, human error, or any number of other factors.
Two terms are used to describe the quality of measurements: precision and accuracy.

17. What is Precision?
Precision is a measure of how closely individual measurements agree with one another.

18. What is Accuracy?
Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.

20. CALCULATING % ERROR actual value  experimental value x 100

21. SAMPLE CALCULATION
In a mass/volume experiment to determine the density of gold, a student calculated the density to be g/mL. The actual value for the density of gold is g/mL. What is the percent error?

22. % ERROR CALCULATION
| – 18.75| x = %
19.32

23. WHAT IS AN ACCEPTABLE % ERROR?
Is 3.0% error a good or a bad result?
That depends upon
The precision of the instruments used
And ultimately the expectation of the teacher.
In this case, 3.0% is very good because of the instruments available in a typical school lab.

24. BEFORE YOU CAN CRUNCH You must know which digits are significant
Because they are going to control the number of digits in a calculated figure

25. WHAT IS A SIGNIFICANT FIGURE?
Significant figures are all the digits in a measurement that are known with certainty plus a last digit that must be estimated.

26. WHICH NUMBERS ARE SIGNIFICANT?
For the purposes of significant figures there are two major categories
Nonzero digits:
1,2,3,4,5,6,7,8,9
Zero digits:

27. NONZERO DIGITS All nonzero digits are significant
3269 cm – 4 significant figures
257 L – 3 significant figures
mm – 7 significant figures

28. ZEROS Zeros take three forms Leading zeros Trapped zeros
Trailing zeros

29. LEADING ZEROS
Leading zeros are zeros that come before the nonzero digits in a number. They are place holders only and are never considered significant.
0.123 L – 3 significant digits
m – 2 significant digits
mL – 4 significant digits

30. TRAPPED ZEROS
Trapped zeros are zeros between two nonzero digits. Trapped zeros are always significant.
101 s – 3 significant figures
20013 m – 5 significant figures
cm – 4 significant figures (the leading zero is not significant)

31. TRAILING ZEROS
Trailing zeros are zeros that follow nonzero digits. They are only significant if there is a decimal point in the number.
mm – 4 significant figures
3000 s – 1 significant figure
250. mL – 3 significant figures
g – 5 significant figures

32. Exact Numbers
Numbers that were not obtained using measuring devices but by counting.
They can also arise from definitions.
They can be assumed to have an infinite number of significant figures.

33. Examples of Exact Numbers
2 in 2r
3 and 4 in ¾ r3
Avogadro’s number is exactly x 1023
One inch is exactly 2.54 cm

34. Now you try How many significant digits in each of the following:
12 apples
3000 m
69 people

35. Answers 1.034 s - 4 significant figures
g significant figures
12 apples exact number
3000 m significant figure
69 people exact number