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Measurement in Science
What do you need to understand
about measurements in science?
1. Quantitative versus qualitative
measurements
2. The metric system
3. Use of official scientific units (SI units –
standard international units)
4. Use of scientific notation (105 etc)
5. Accuracy versus precision versus error
6. Use of significant figures
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
Science (usually) uses the
METRIC system
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)
1 metre =
= 10 dm
= 100 cm
= 1000 mm
1 kg =
= 10 dg
= 1000 g
= 1 000 000 mg
1 mm =
= 0.1 cm
= 0.001 m
1 mg =
= 0.001 g
= 0.000 001 kg
Standard International Units
Measuring distance-length: METRE
Time is measured in SECONDS
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)
Mass is not equivalent to weight!
•
•
•
•
MASS
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
• 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).
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
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
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
Scientific notation
Simple – it’s the method scientist use to neatly
write very BIG or very small numbers.
Scientific notation
Significant Figures
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)
Precision or accuracy?
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
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
Significant Figures – Counting
Rules
• Non-zero digits are ALWAYS Significant
• Leading zeros are NEVER significant
– 0.000036 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 2.500 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 15.10 have FOUR Significant Figures
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: 32701.00
= 3.270100 X 104
Note that in this example, the two zeros following the decimal point are
also considered as significant…
Decimal places versus significant
figures
When we round to decimals, we start counting
as soon as we reach the decimal point.
Round 17.46789 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
Significant Figures
When we round to significant figures, we start
counting as soon as we reach a number that is not
zero
Round 17.46789 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 17.46789 to 2 decimal places=17.00
Round to
1 sf
43 07 08 50 03 07
Look at the next number
It’s more than 4 so we round
up!
Round to
3 sf
3 7 8 04 03 07
Look at the next number
It’s less than 5 so we round down!
Round to
2 sf
0 . 0 0 2 98 9
Look at the next number
It’s more than 4 so we round
up!
Round to
3 sf
0 . 0 0 2 0 98 7
Look at the next number
It’s more than 4 so we round
up!
Rounding to Significant Figures
Main
1. 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
2.
i. 1000 1500 1460
ii. 200 160 157
iii. 40 37 37.1
iv. 6 6.1 6.09
v. 0.006 0.0064 0.00640
3.
a) 4.7
b) 0.058
c) 0.19
d) 540
Significant Figures –
Adding/Subtracting
The answer cannot have more decimal places than
the least number of decimal places in the calculation
• Add 15.1 to 3
• The answer is 18
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
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?
Rounding to Significant
Figures (sig fig or s.f)
10 multiple choice
questions
Round-
0.23 to 1 s.f
A)
0.3
B)
2
C)
0.2
D)
3
Round-
0.045 to 1 s.f
A)
0.04
B)
0.1
C)
0.0
D)
0.05
Round-
623 to 1 s.f
A)
600
B)
620
C)
630
D)
700
Round-
5328 to 1 s.f
A)
5300
B)
5000
C)
5330
D)
6000
Round-
0.005136 to 2 s.f
A)
0.01
B)
0.0050
C)
0.00514
D)
0.0051
Round-
426.213 to 2 s.f
A)
426.21
B)
430
C)
400.00
D)
420
Round-
3002.01 to 3 s.f
A)
300
B)
3000
C)
3010
D)
3002.0
Round-
983.4 to 1 s.f
A)
100
B)
900
C)
980
D)
1000
Round-
0.00456 to 2 s.f
A)
0.0045
B)
0.004
C)
0.0046
D)
0.00
Round-
36345.3 to 3 s.f
A)
36300
B)
4000
C)
36000
D)
45300
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?
A.
B.
C.
D.
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
The dart
thrower is
A.
B.
C.
D.
accurate but not precise
precise but not accurate
both accurate and precise
neither accurate nor precise
The dart
thrower is
A.
B.
C.
D.
accurate but not precise
precise but not accurate
both accurate and precise
neither accurate nor precise
The dart
thrower is
A.
B.
C.
D.
accurate but not precise
precise but not accurate
both accurate and precise
neither accurate nor precise
What is the correct
reading on this cylinder?
A.
B.
C.
D.
E.
30 cm3
32 cm3
32.0 cm3
34 cm3
34.0 cm3
What is the uncertainty
in this reading?
A.
B.
C.
D.
± 0.05 cm
± 0.10 cm
± 0.20 cm
± 1.00 cm
What is the sum 3.041 + 0.81?
A. 3
B. 4
C. 3.9
D. 3.85
E. 3.851
What is the product 8.2 x 13.7?
A.
B.
C.
D.
E.
100
110
112
112.3
112.34
What is 31 times the
answer to the
previous problem?
A. 3400
B. 3410
C. 3482.54
D. 3500