Transcript Significant Figures

Significant Figures
& Rounding
Chemistry A
Introduction
Precision is sometimes limited to the
tools we use to measure.
For example, some digital clocks
display only hours and minutes
(12:00), so you can only read it to the
nearest minute.
With a stopwatch we can read up to
the nearest hundredth of a second.
So scientists indicate the precision of
measurements by the number of
digits they report.
For example, a value of 3.25g is more
precise than a value of 3.3 g.
The digits that are reported are the
Significant Figures.
Significant Figures
Significant Figures include all known
digits plus one estimated digit.
There are rules we need to follow
when dealing with Significant Figures.
Rules for Recognizing Sig. Figs.
1. Non-zero numbers are always
significant.
7.23  has three
2. Zeros between non-zero numbers are
always significant.
60.5  has three
3. All ending zeros to the right of the
decimal are significant.
6.20  has three
Rules for Recognizing Sig. Figs.
4. Zeros that act as placeholders not
significant. Convert to sicentific notation
0.000253 & 432000  each have three
5. Counting numbers and defined constants
have an infinite number of significant
figures.
π = 3.14
Practice
Determine the Significant Figures in the
following numbers.
508.0
4 sig. figs.
807000
3 sig. figs.
0.000482
3 sig. figs.
3.1587 x 10-8
5 sig. figs.
Rounding Numbers
Suppose you divide 22.44 by 14.2 on
you calculator. The answer you get is
1.5802817.
Do you write all of that number down
as your answer?
No, because your answer should
have no more significant figures than
the data with the fewest sig. figs.
So your answer should be 1.58
Rules for Rounding Numbers
If the number right next to the last sig.
fig. is less than 5, don’t change the
last significant figure.
2.532  2.53
If the number right next to the last sig.
fig. is greater than 5, round up the last
significant figure.
2.536  2.54
Rules for Rounding Numbers
If the number right next to the last sig.
fig. is equal to 5 and is followed by a
non-zero, round up the last significant
figure.
2.5351  2.54
Rules for Rounding Numbers
If the number right next to the last sig.
fig. is equal to 5 and is not followed by
a non-zero, look at the last significant
figure.
If odd, round up.
If even, don’t round up.
2.5350  2.54 but 2.5250  2.52
Practice
Round to 4 significant figures
84791
84790
38.5432
38.54
256.75
256.8
4.9356
4.936
Adding & Subtracting
When adding or subtracting, answer
must have the same amount of
numbers to the right of the decimal
point as the value with the fewest
numbers to the right of the decimal.
28.0
23.538
+ 25.68
77.218  77.2
Practice
43.2 + 51.0 + 48.7 =
142.9
93.26 – 81.14 =
12.12
258.3 + 257.11 + 253 =
768
Multiplying & Dividing
Your answer must have same amount
of numbers as the value with the
fewest significant figures.
3.20 x 3.65 x 2.05 = 23.944
23.944  23.9
Practice
24 x 3.26 =
78
120 x 0.10 =
12
4.84/ 2.4 =
2.0
168/ 58 =
2.9