1. Measurement in Science

3. What do you need to understand about measurements in science?
Quantitative versus qualitative measurements
The metric system
Use of official scientific units (SI units – standard international units)
Use of scientific notation (105 etc)
Accuracy versus precision versus error
Use of significant figures

4. Qualitative versus quantitative measurements
Qualitative measurements
Use words (not numbers) to describe what happened
Words may be descriptive and not necessarily specific
Quantitative measurements
Uses NUMBERS
Uses UNITS
Can be accurate or inaccurate
Can be precise or imprecise

5. Science (usually) uses the METRIC system

7. Essential metric prefixes
Kilo (k) = 1000 (one thousand, 103)
Deci (d) = 1/10 (one tenth, 10-1)
Centi (c) = 1/100 (one hundredth, 10-2)
Milli (m) = 1/1000 (one thousandth, 10-3)
Micro () = (one millionth, 10-6)
Nano (η) = (one billionth, 10-9)

8. 1 metre = = 10 dm = 100 cm = 1000 mm 1 mm = = 0.1 cm = 0.001 m
1 kg = = 10 dg = 1000 g = mg 1 mg = = g = kg

9. Standard International Units

10. Measuring distance-length: METRE

11. Time is measured in SECONDS

12. MASS is measured in kilograms (g)
Mass is a measure of the quantity of matter
Mass is constant, regardless of location
Measured in kg
(NB: Weight is a force that measures the pull by gravity- it changes with location)

13. Mass is not equivalent to weight!
Is measured in kg
Reflects how much matter something contains
Is closely related to inertia
Cannot be measured directly
WEIGHT
Is measured in NEWTONS (= 1 kg.ms-1)
Is a force measurement which measures how strongly gravity is pulling on an object

14. Scales show an estimate of your mass based on the force your body exerts on it.
And to find out how much force your body is exerting on the scales, multiply by 9.8 (to convert kg into Newtons).

16. Measuring Temperature: KELVIN
Kelvin scale (or absolute scale)
Named after Lord Kelvin
K = oC + 273
A change of one degree Kelvin is the same as a change of one degree Celsius
No degree sign is used

17. Temperature Scales Water freezes at 273 K Water boils at 373 K
0 K is called absolute zero, and equals –273 oC
Absolute zero is the temperature at which gas molecules stop moving

18. Non SI temperature scale - CELSIUS
Celsius scale- named after Swedish astronomer Anders Celsius
Uses the freezing point (0 oC) and boiling point (100 oC) of water at atmospheric pressure as references
Divided into 100 equal intervals, or degrees Celsius

20. Scientific notation
Simple – it’s the method scientist use to neatly write very BIG or very small numbers.

22. Scientific notation

25. Significant Figures

26. How sure can we be about our measurements?
We seek to make our measurements as accurate and precise as possible
Accuracy – how close a measurement is to the true value
Precision – how close the measurements are to each other (reproducibility)

27. Precision or accuracy?

28. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
30.5
31.5
nearest to 30.5
measure to 1 dp; one more dp than smallest division 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
30.55
30.65
nearest to 30.55
measure to 2 dp; one more dp than smallest division

29. Applying Precision
Scientists use significant figures to show precision of a measured quantity
Significant figure: ‘each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit’
In science, numbers are always rounded to a defined number of significant figures

30. Significant Figures – Counting Rules
Non-zero digits are ALWAYS Significant
Leading zeros are NEVER significant
has TWO Significant Figures
Trailing zeros may or may not be significant
2500 may have TWO or FOUR Significant Figures
2.5 X 103 has 2 s.f., while X 103 has 4 s.f.
Zeros ‘in between’ Non-Zeros are significant
2501 and 2003 have FOUR Significant Figures
Zeros after a decimal point ARE SIGNIFICANT
They do not begin the number
25.00 and have FOUR Significant Figures

31. How many significant figures are there in a number?
An EASY way to decide is to convert the number to SCIENTIFIC NOTATION (but keep and consider any zeros following a decimal point)… The number of digits in your ‘mantissa’ is your number of significant figures For example: = X 104 Note that in this example, the two zeros following the decimal point are also considered as significant…

32. Decimal places versus significant figures
When we round to decimals, we start counting as soon as we reach the decimal point.
Round to 2 decimal places
1 decimal place
2 decimal places, this will stay a 6 or go to a 7 depending on what the next number is

33. Significant Figures
When we round to significant figures, we start counting as soon as we reach a number that is not zero
Round to 2 significant figures
1 significant figure
2 significant figures, this will stay a 7 or go to a 8 depending on what the next number is
All the numbers after will become zero
Round to 2 decimal places=17.00

34. It’s more than 4 so we round up!
Round to 1 sf 3 7 8 5 4 3 7
Look at the next number
It’s more than 4 so we round up!

35. It’s less than 5 so we round down!
Round to 3 sf 3 7 8 4 3 7
Look at the next number
It’s less than 5 so we round down!

36. It’s more than 4 so we round up!
Round to 2 sf . 2 9 8 9
Look at the next number
It’s more than 4 so we round up!

37. It’s more than 4 so we round up!
Round to 3 sf . 2 9 8 7
Look at the next number
It’s more than 4 so we round up!

38. Rounding to Significant Figures
Main
When you are rounding to decimal places you start counting after the decimal point, but with significant figures you start counting at the first non zero number
4.7
0.058
0.19
540

39. Significant Figures – Adding/Subtracting
The answer cannot have more decimal places than the least number of decimal places in the calculation
Add to 3
The answer is 18

40. Significant Figures – Multiplication/Division
Based on the given values, or what you think are measured values, round your answer so that it has the same number of significant figures as the input (or given) with the least number of significant figures
Multiply 2.0 and 3.01
Answer in correct significant figures is 6.0

41. 27
26.5≤x<27.5
27.0
26.95≤x<27.05
27.00
26.995≤x<27.005
Which is the measurement with the highest precision and probably the most accurate?

42. Rounding to Significant Figures (sig fig or s.f)
10 multiple choice questions

43. Round-
0.23 to 1 s.f
0.3 2 A) B)
0.2 3 C) D)

44. Round-
0.045 to 1 s.f
0.04
0.1 A) B)
0.0
0.05 C) D)

45. Round-
623 to 1 s.f
600
620 A) B)
630
700 C) D)

46. Round-
5328 to 1 s.f
5300
5000 A) B)
5330
6000 C) D)

47. Round-
to 2 s.f
0.01
0.0050 A) B)
0.0051 C) D)

48. Round-
to 2 s.f
426.21
430 A) B)
400.00
420 C) D)

49. Round-
to 3 s.f
300
3000 A) B)
3010
3002.0 C) D)

50. Round-
983.4 to 1 s.f
100
900 A) B)
980
1000 C) D)

51. Round-
to 2 s.f
0.0045
0.004 A) B)
0.0046
0.00 C) D)

52. Round-
to 3 s.f
36300
4000 A) B)
36000
45300 C) D)

53. A duck is exactly 10. 0 cm tall
A duck is exactly 10.0 cm tall. The duck was measured several times by several people. Which of the following data sets is most precise?
8.1, 8.0, 8.2, 8.0
9.7, 10.0, 10.9, 10.3
9.1, 9.0, 10.8, 10.6
7.9, 10.0, 11.4, 10.5

54. The dart thrower is accurate but not precise precise but not accurate
both accurate and precise
neither accurate nor precise

55. The dart thrower is accurate but not precise precise but not accurate
both accurate and precise
neither accurate nor precise

56. The dart thrower is accurate but not precise precise but not accurate
both accurate and precise
neither accurate nor precise

57. What is the correct reading on this cylinder?
30 cm3
32 cm3
32.0 cm3
34 cm3
34.0 cm3

58. What is the uncertainty in this reading?
± 0.05 cm
± 0.10 cm
± 0.20 cm
± 1.00 cm

59. What is the sum ? 3 4
3.9
3.85
3.851

60. What is 31 times the answer to the previous problem?
What is the product 8.2 x 13.7?
What is 31 times the answer to the previous problem?
100
110
112
112.3
112.34
3400
3410
3500