Transcript Significant Figures

Significant Figures
Chemistry
What is a significant figure?
• There are 2 kinds of
numbers:
–Exact: the amount of
money in your account.
Known with certainty.
What is a significant figure?
Approximate: weight, height,
anything MEASURED.
No measurement is perfect.
When to use Significant Figures
• When a measurement is
recorded, the
instrument used
determines what digits
are written down.
When to use Significant Figures
–If you measured the
width of a paper with
your ruler you might
record 21.72 cm.
To a mathematician 21.72,
or 21.720 is the same.
But, to a scientist 21.72 cm and
21.720 cm is NOT the same
• 21.700 cm to a scientist means
the measurement was made with
a ruler with markings at onehundredth of a centimeter.
• Notice that the number has a
value in the one-thousanths
place?
That is the estimated digit.
But, to a scientist 21.72 cm and
21.720 cm is NOT the same
• If you used an ordinary
metric ruler, the smallest
marking is the mm (or onetenth of a centimeter, so your
measurement has to be
recorded as 21.72 cm.
• Again, the LAST digit is
always estimated.
How do I know how many Sig Figs?
• Rule: All digits are
significant starting with the
first non-zero digit on the
left.
• So when you see zeroes
before a real number,
THEY DON’T COUNT!
How do I know how many Sig Figs?
st
• 1 Exception to Rule: In
whole numbers that end in
zero, the zeros at the end
are not significant.
• If you see a decimal point,
this exception no longer
applies!
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
How do I know how many Sig Figs?
• If zeros are
“sandwiched” between
non-zero digits, the
zeros are significant.
How do I know how many Sig Figs?
• If zeros are at the end of
a number that has a
decimal, the zeros are
significant.
How do I know how many Sig Figs?
• End zeroes after a
decimal are showing
how accurate the
measurement or
calculation are.
How many sig figs here?
•
•
•
•
•
•
1.2
2100
56.76
4.00
0.0792
7,083,000,000
•
•
•
•
•
•
2
2
4
3
3
4
How many sig figs here?
•
•
•
•
•
•
3401
2100
2100.0
5.00
0.00412
8,000,050,000
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•
•
•
•
•
4
2
5
3
3
6
PRACTICE WITH SIGNFICANT
FIGURES AND ESTIMATED
DIGITS
• In a few minutes, we will
talk about what to do when
you are calculating.
What about calculations with
sig figs?
• Rule: When adding or
subtracting measured
numbers, the answer can have
no more places after the
decimal than the LEAST of
the measured numbers.
Add/Subtract examples
• 2.45cm + 1.2cm = 3.65cm,
• Round off to
= 3.7cm
• 7.432cm + 2cm = 9.432
round to
 9cm
Multiplication and Division
• Rule: When multiplying
or dividing, the result
can have no more
significant figures than
the least reliable
measurement.
A couple of examples
• 56.78 cm x 2.45cm = 139.111
• Round to
 139cm2
• 75.8cm x 9.6cm = ?
2
cm
The End
Happy Calculating!