1. Scientific Measurement
Chapter 3
Scientific Measurement

2. Types of measurement Quantitative- use numbers to describe
Qualitative- use description without numbers
4 feet
extra large
Hot
100ºF

3. Scientists prefer Quantitative- easy check
Easy to agree upon, no personal bias
The measuring instrument limits how good the measurement is

4. Scientific Notation
Scientist often work with really BIG or really SMALL numbers
A mol of iron contains 602,000,000,000,000,000,000,000 atoms of iron
A proton has a mass of 0.000,000,000,000,000,000,000,001,670 g
Scientific, or exponential notation makes numbers easier to work with

5. A mol of iron contains 1.06 × 1023 atoms
A proton has a mass of 1.67 × g
Written as a product of 2 numbers
A coefficient and 10 raised to a power
For the iron (Fe), 1.06 is the coefficient
The power of ten, or exponent is 23
Exponent – or +
If the coefficient is…
>10 +
< 10 -

6. Multiplication and Division
Multiply coefficients
Add exponents
Example
(2.0 × 1013) × (3.0 × 102)
Divide coefficients
Subtract coefficient in denominator (b) from the numerator (top)
(2.0 × 1013) ÷ (3.0 × 102)

7. Addition and Subtraction
Make the exponents the same by determining where the decimal is in the original number
Line up the decimals to add or subtract
Example
(2.0 × 1013) + (3.0 × 102)
(2.0 × 1013) - (3.0 × 102)

8. How good are the measurements?
Scientists use two word to describe how good the measurements are
Accuracy- how close the measurement is to the actual value
Precision- how well can the measurement be repeated

9. Let’s use a golf anaolgy

10. Accurate? No
Precise?
Yes

11. Accurate?
Yes
Precise?
Yes

12. Precise? No
Accurate?
Maybe?

13. Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it
It is important to realize that a measurement always has some degree of uncertainty.

14. In terms of measurement
Three students measure the room to be m, 10.3 m and 10.4 m across.
Were they precise?
Were they accurate?

15. Error Error = accepted – experimental value
The percent error of a measurement is the absolute value.
Percent Error
| error |
× 100%
accepted value

16. Example
A student calculated the density for an unknown metal as g/cm3. The metal was later identified as iron with an accepted density value of g/cm3.
What was the student’s percent error?

17. Answer: Experimental value=8.163 Accepted value = 7.8724=
x100 =
7.8724
3.987

18. Significant figures (sig figs)
How uncertain are our measurements?
When we measure something, we can (and do) always estimate between the smallest marks. 2 1 3 4 5

19. Significant figures (sig figs)
The better marks the better we can estimate.
Scientist always understand that the last number measured is actually an estimate 1 2 3 4 5

20. Sig Figs
What is the smallest mark on the ruler that measures cm?
142 cm?
140 cm?
Here there’s a problem, does the zero count or not?
They needed a set of rules to decide which numbers count-

21. Which zeros count?
Trailing zeros-Those at the end of a number before the decimal point don’t count
12400
Leading zeros-If the number is smaller than one, zeroes before the first number don’t count
0.045

22. Sig fig Rules Nonzero digits are always significant.
46.3 has 3 sig figs
Zeros between nonzero digits are significant.
40.07 has 4 sig figs
Zeros in front of nonzero digits (leading zeros) are not significant.
has only one sig fig.

23. Sig Fig Rules cont
Zeros both at the end of a number and to the right of a decimal point are significant.
85.00
Zeros both at the end of a number but to the left of a decimal point may not be significant. If a zero has not been measured or estimated, it is not significant. A decimal point place after zeros indicates that the zeros are significant. ( )

24. Problems 50 is only 1 significant figure
if it really has two, how can I write it?
A zero at the end only counts after the decimal place
Scientific notation
5.0 x 101
now the zero counts.

25. Sig Figs
Scientists always report values using significant figures. The significant figures of a measurement or a calculation consist of all the digits known with certainty as well as one estimated or uncertain digit.
Counting -there is no uncertainty.
Conversion factors-there is no uncertainty.

26. Sig figs. How many sig figs in the following measurements? 458 g

27. Sig Figs.
405.0 g
4050 g
0.450 g g g
Next we learn the rules for calculations

28. More Sig Figs

29. Adding and subtracting with sig figs
The last sig fig in a measurement is an estimate.
Your answer when you add or subtract can not be better than your worst estimate.
have to round it to the least place of the measurement in the problem

30. Rounding rules look at the number behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
round to four sig figs
to three sig figs
to two sig figs
to one sig fig

31. Measurements of Length, Volume and Mass
Metric system is the preferred measurement system among scientists.
International System started in 1960 as a comprehensive system to be used worldwide. It is based on the metric system and is derived from the metric system.

32. SI System SI system uses prefixes-memorize!!
SI unit of length is the meter
SI unit of mass is the kilogram or gram with the metric system
SI unit of volume is the liter
Remember 1ml or cc = 1 g

33. For example
27.93
6.4 +
First line up the decimal places
27.93
6.4 +
27.93
6.4
Then do the adding
Find the estimated numbers in the problem
34.33
This answer must be rounded to the tenths place

34. Practice
(6.0 x 102) – (3.8 x 103)
(6.0 x 10-2) – (3.8 x 10-3)

35. Multiplication and Division
Rule is simpler
Same number of sig figs in the answer as the least in the question
3.6 x 653
2350.8
3.6 has 2 s.f. 653 has 3 s.f.
answer can only have 2 s.f.
2400

36. Multiplication and Division
Same rules for division
practice
4.5 / 6.245
4.5 x 6.245
x .043
3.876 / 1983
16547 / 714

37. Metric Length – meter, more than a yard - m
Mass - grams - about a raisin - g
Time - second - s
Temperature - Kelvin or ºCelsius K or C
Energy - Joules- J
Volume - Liter - half a two liter bottle- L
Amount of substance - mole - mol

38. Temperature Fahrenheit scale-Water boils at 212 and freezes at 32
Celsius Scale-Water boils at 100 and freezes at 0
Kelvin Scale-Water boils at 373 and freezes at 273.

39. Measuring Temperature
0ºC
Measuring Temperature
Celsius scale.
water freezes at 0ºC
water boils at 100ºC
body temperature 37ºC
room temperature ºC

40. Measuring Temperature
273 K
Measuring Temperature
Kelvin starts at absolute zero (-273 º C)
degrees are the same size
C = K -273
K = C + 273
Kelvin is always bigger.
Kelvin can never be negative.

41. Converting Between Temp Scales
Tc +273 = Tk
Tk-273 = Tc
Tf = 1.8 (Tc) + 32
Tc = Tf – 32
1.8

42. Which is heavier?
it depends

43. Density How heavy something is for its size
The ratio of mass to volume for a substance
D = M / V
Independent of how much of it you have
gold - high density
air low density.

44. Density of water 1 g of water is 1 mL of water.
density of water is 1 g/mL
at 4ºC
otherwise it is less

45. Floating Lower density floats on higher density.
Ice is less dense than water.
Most wood is less dense than water
Helium is less dense than air.
A ship is less dense than water

46. Specific Gravity
Compares density of something to a reference at same temp. (i.e. water)
Density of a substance
Specific Gravity=
Density of Water
Units cancel
What is the specific gravity of gold? (D=19.3 g/cm3)

47. Converting k h dk d c m
how far you have to move on this chart, tells you how far, and which direction to move the decimal place.
The box is the base unit, meters, Liters, grams, etc.

48. k h d c m Conversions 5 6 dk Change 5.6 m to millimeters
starts at the base unit and move three to the right.
move the decimal point three to the right 5 6

49. k h d c m Conversions dk convert 25 mg to grams convert 0.45 km to mm
convert 35 mL to liters
It works because the math works, we are dividing or multiplying by 10 the correct number of times

50. Conversions k h dk d c m
Change 5.6 km to millimeters

51. Dimensional Analysis Unit 1 x conversion factor = Unit 2
To convert from one unit to another:
Use the equivalence statement
Choose the appropriate conversion factor
Multiply the quantity to be converted by the conversion factor.
Check for correct # of sig figs.

52. Calculating The formula tells you how units will be g/mL or g/cm3
A piece of wood has a mass of 11.2 g and a volume of 23 mL what is the density?
A piece of wood has a density of 0.93 g/mL and a volume of 23 mL what is the mass?

53. Calculating
A piece of wood has a density of 0.93 g/mL and a mass of 23 g what is the volume?
The units must always work out.
Algebra
Get the thing you want by itself, on the top.
What ever you do to onside, do to the other