Precision and accuracy in
measurements
• Shows accuracy, but
not precision
• Shows precision but
not accuracy
Label each experiment. Indicate
whether the diagram illustrates
precision, accuracy, both, or neither.
Accuracy and Precision in
measurement
• Accuracy refers to the agreement of
a particular value or measurement
with the true or accepted value.
• Precision refers to how close the
values or measurements are to
each other.
Uncertainty in Measurement
A digit that must be estimated is called
uncertain. A measurement always
has some degree of uncertainty.
When you measure any quantity, the
last digit is estimated . In science, you
MUST always estimate the last digit.
This is called reading to the “precision
of the instrument”.
STEPS TO READING AN
INSTRUMENT CORRECTLY
1. Determine the value of the markings on the
instrument
2. Read correctly to that mark.
3. Then estimate the next number. If a
measurement falls right on a marking, you
MUST estimate the next digit as “ZERO”.
4. Remember!!!!! Your measurement MUST
always include an estimated digit.
Reading graduated cylinders
(read the bottom of the meniscus)
100 mL graduated cylinder
Try Again
25 mL graduated cylinder
How long is the green line?
0
10
0
0
20
30
2
50
200
100
1
40
3
4
60
70
300
5
6
7
90
50
80
40
70
30
60
20
50
10
40
0
• http://antoine.frostburg.edu/cgibin/senese/tutorials/sigfig/index.cgi
COUNTING SIG. DIGS.
WHAT EVERYONE SHOULD
KNOW
Rules for Counting Significant
Figures - Overview
1. Nonzero integers
2. Zeros
• leading zeros
• captive zeros
• trailing zeros
3. Counting numbers
4. Equivilancies
NON-ZERO NUMBERS
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ARE ALWAYS SIGNIFIGANT
45.336 g
5
25.3 mL
3
45 cm
2
12922 cal
5
CAPTIVE ZEROS
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BETWEEN NON-ZERO NUMBERS
ARE ALWAYS SIGNIFICANT
25.03 g
4
25,001 m
5
145.06 kg
5
5.04 m
3
LEADING ZEROS
• IN FRONT OF NON-ZERO NUMBERS
• ARE NEVER SIGNIFICANT
• Start counting at the 1st NONZERO
number
• 0.0025 g
2
• 0.235 mL
3
• 0.0003 cm
1
• 0.000007631 mm 4
TRAILING ZEROS
• COME AFTER NON-ZERO DIGITS
• ARE SIGNIFICANT IF THERE IS A
DECIMAL POINT IN THE NUMBER
• 25,000 kg
2
• 25,000.00 g
7
• 2100 mL
2
• 57.0 m
3
COUNTING NUMBERS
• ARE INFINITELY SIGNIFICANT
• WILL NEVER DETERMINE SIG. DIGS. IN
ANSWERS
• 2 sheets of paper
• 10 pennies
• There are 26 students in my class.
EQUIVILANCIES
• MEASUREMENTS THAT ARE EQUAL TO
EACH OTHER
1 cm = 10 mm
1000 g = 1kg
1 L = 1000 mL
1.00 meters = 100.cm
• ARE INFINITELY SIGNIFICANT
• ARE NOT USED TO DETERMINE SIG. DIGS.
IN ANSWER
Fill in Significant digit practice
Example
Significant Figures
Give the number of significant figures for
each of the following.
a. A student’s extraction procedure on tea
yields 0.0105 g of caffeine.
b. A chemist records a mass of 0.050080 g
in an analysis.
c. In an experiment, a span of time is
determined to be 8.050 x 10-3 s .
Significant digits worksheet
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Chemistry I
This worksheet is divided into several parts. Your
instructor will assign certain sections as homework.
Counting significant digits
a. 3.977 g __4__Rule:_Nonzero integers are always
significant
b. 0.0033 cm__2__ Rule:_Leading zeros are never
significant
c. 10045 cal__5___Rule:_Captive zeros are always
significant
d. 14.0 0C _3____Rule:_Trailing zeros are significant if
there is a decimal point
e. 1200 mL__2___Rule:_Trailing zeros are not significant if
there is not a decimal point
Page 53 #4
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Student 1 Student 2 Student 3
Trial 1
2.60cm
2.70cm
2.75cm
Trial 2
2.72cm
2.69cm
2.74cm
Trial 3
2.65cm
2.71cm
2.64cm
Average 2.66cm
2.70cm
2.71cm
• Correct answer is (a.) Student 2 is both
precise and accurate
Nature of Measurement
•
Measurement - quantitative observation
consisting of 2 parts
Part 1 – number
Part 2 - scale (unit)
•
Examples:
20 grams
6.63   Joule· seconds
Part 1: Rules for Significant Figures
in Mathematical Operations
Addition and Subtraction: # sig figs in the
answer equals the number of decimal
places in the least precise measurement
(one with least number of decimal places
to the right of the decimal point)
6.8 cm
+ 11.934 cm
18.734 cm  18.7 cm (3 sig figs)
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division: # sig digits in the
answer are equal to the measurement with the least
number of sig digits used in the calculation.
6.38 cm  2.0 cm = 12.76 cm2  13 cm2 (2 sig figs)
4.92 cm
3.0 cm
= 1.64  1.6 (2 sig figs)
UNITS ON ANSWERS
• Units in the answer are derived from units in the
problem
• When adding or subtracting, the unit is the
same as in the problem.
• Multiplying like units gives a square measurement
(2 cm x 2 cm = 4 cm2 ) OR
a cubic measurement
(2 cm x 2 cm x 2 cm = 8 cm3)
• Multiplying unlike units means that both units
appear in the answer separated by a •
22.4 L
x
1.00 atm
=
22.4 L• atm
• Dividing like units cancels the unit--------2 cm
2 cm = 1
• If you divide unlike units all units MUST
appear in the answer.
• 8.0 g = 2.0 g/mL
4.0 mL
• (22.4 L)(1.00 atm) = 0.0891L • atm
(273 K)(1.00 mol)
K • mol
MIXED OPERATIONS
• Sometimes a calculation involves
addition/subtraction AND multiplication/division.
Then 2 roundings must take place because there
are
2 different rules.
• 25.0 mL – 15.0 mL = 5
2 mL
First : 25.0 mL – 15.0 mL = 10.0 mL
then : 10.0mL =
2 mL
5 (no units)
APPLYING ROUNDING RULES
• If the digit to the right of the last sig. digit is
< 5, do not change the last sig. digit
•
2.532  2.53
• If the digit to the right of the last sig. digit is
> than or = to 5, round up.
• 2.535  2.54
• If the digits to the right of the last sig. digit
are 49 you only look at the 4 and do not
change the last sig. digit.
2.5349  2.53
More Rounding Info
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123.456
ones
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123.456
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tens
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123.456
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tenths
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123.456
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hundredths
123.456
thousandths
Sig. Digit WS II
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( 3 sig. digits)
a) 0.02443 kcal = 0.0244 kcal
b) 95.56 g = 95.6g
c) 57.048 m = 57.0 m
d) 12.17 C = 12.2 C
e) 1764.9 ml = 1760 ml
f) 8.859 km = 8.86 km
g) 45,560 mm = 45,600 mm
Sig. Digit WS III & IV A
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e) 43.13g = 43.1g (tenths)
f) 155 m = 160 m ( tens)
g) 8.859 km = 8.86 km (hundredths)
h) 124.78 g = 125 g (ones)
67.14 kg + 8.2 kg = 75.3 kg
87.3 cm - 1.655 cm = 85.6 cm
8.2 cm - 7.11 cm = 1.1 cm
0.042g - 0.02g m = 0.02 g
853.2 mL + 627.443 mL = 1480.6 mL
12.2 0C + 18.54 0C = 30.7 0C
.