Download WorkingWithNumbers1 SigFigs

Chemistry 11HL
Unit 1 / IB Topic 1
Working With Numbers 1
Significant Figures
Chemistry is an “empirical” subject – and that means understanding the
chemical world by doing experiments.
One very important aspect of experimentation is MEASUREMENT. Knowing
how to make precise and reliable measurements, how to record those
measurements in a clear organized manner and how to work with and use the
measurements to find relationships will make your life as an IB Chemistry
student much easier. Really. Honestly. Truly.
“SIG FIGS” ARE
BIG!
“Sig figs” really means SIGNIFICANT FIGURES or SIGNIFICANT DIGITS. They are very
important to scientists when they communicate their findings to the world.
So why do we care about “sig figs” so much? One answer lies in a question many students ask
when doing calculations. Try this calculation:
26.5 ÷ 29 = ___________
What are you going to do with this answer?
A more important reason for lovin’ sig figs has to do with how we measure things. We will look
at this idea in more detail in the next class. But for a sneak preview, think about how you would
record the measurement at the arrow:
your reading:
acceptable readings:
unacceptable readings:
The number of digits you write in a measured value tells you how PRECISE your measurement
is. Is it just “close to” a certain value, or is it really really “exact”? The number of significant
figures in your measurement helps others decide how precise your value is.
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Chemistry 11HL
Unit 1 / IB Topic 1
SIG FIG RULES!
Use these rules to decide how many significant figures are in a numerical value:
1. Digits from 1 – 9 are always significant.
Examples:
23 kg
79.42 mL
923 m
2. Anything you count is significant.
Examples:
1725 students
40 classrooms
18 cookies
3. Zeros between two other non-zero digits are always significant.
Examples:
30.5 cm
2009 years
3.0205 h
4. Zeros after the decimal are significant if a digit between 1 and 9 precedes it.
Examples:
9.00 g
37.0 ˚C
5. Zeros at the end of a whole number are NOT significant.
Examples:
800 m
30 L
6. Leading zeros are not significant (they are only there to indicate the location of the
decimal point).
Examples:
0.82 g
0.003 s
How many significant digits are in the following? State the rule you use to help you
decide on your answer.
a) 23.7 cm
b) 107 L
c) 40 chairs
d) 4301.0 mm
e) 0.00045 g
f) 600 years
g) 00.00200 V
h) 100.0001010 g
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Chemistry 11HL
Unit 1 / IB Topic 1
CALCULATIONS AND SIGNIFICANT FIGURES
RULE 1: MULTIPLICATION AND DIVISION
When multiplying or dividing, round your answer to the least number of
SIGNIFICANT FIGURES in the values used in the calculation.
eg:
22.378 cm x 3.10 cm ÷ 85.75 cm =
RULE 2: ADDITION AND SUBTRACTION
When adding or subtracting numbers, round your answer to match the least number of
DECIMAL PLACES in the values used in the calculation.
eg:
3.76 g + 14.83 g + 2.1 g =
TRY THESE:
a)
4.64 + 3.2 =
b)
22.4420 + 56.981 =
c)
67.5 – 0.009 =
d)
50.0 x 2.63 =
e)
(2.3)(3.45)(7.42) =
f)
1.0007 ÷ 0.009 =
g)
51 ÷ 7.4 =
h)
208 ÷ 9.036 =
i)
(8.852 x 9.2) ÷ (4.821 x 7) =
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Chemistry 11HL
Unit 1 / IB Topic 1
PRACTICE PROBLEMS
1.
2.
3.
Give the number of significant digits in each of the following measurements:
a)
3.782 g
b)
0.00390 s
c)
75.2 mL
d)
19,000 J
e)
6.022 x 10
f)
23 students
g)
53.50 mL
h)
2.0703 x 10
23
-10
mol
Round off the following numbers to three significant digits. Express your answers in
scientific notation where appropriate.
a)
120 000
b)
43.619
c)
5.0457
d)
2.8029 x 10
e)
0.000 82057
f)
6.00098 x 10
-3
4
Calculate these values and record the final answer to the correct number of significant
figures:
a)
23.4 x 14
b)
0.005 - 0.0007
c)
7.895 + 3.4
d)
7.895 ÷ 34
e)
0.0945 x 1.47
f)
0.2 ÷ 0.0005
g)
0.0050 – 0.0007
h)
(3.1 x 10 ) x (4.821 x 10 )
i)
15.0 – 7.2
j)
0.25 ÷ 28.02
3
-2
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