Download Significant Figures (sig figs)

Significant Figures
Chemistry
Exact vs approximate
There are 2 kinds of numbers:
1. Exact: the amount of money in your
account. Known with certainty.
2. Approximate: weight, height—
anything MEASURED. No
measurement is perfect.
Estimate of Uncertainty
• When a measurement is recorded the
digits that are dependable are written
down PLUS the estimate of uncertainty.
• You estimate to one place beyond the
smallest scale division.
Math versus Science
If you measured the width of a paper with your
ruler you might record it as 21.7cm.
To a mathematician 21.70, or 21.700 is the same
as 21.7.
But to a scientist means the measurement of
21.700 means it is accurate to within one
thousandth of a cm.
But, to a scientist 21.7cm and
21.70cm is NOT the same
• If you used an ordinary ruler, the smallest marking
is the mm, so your measurement has to be
recorded as 21.7cm.
• If your measurement is exactly 21.7 cm, your
estimate of uncertainty is one place past the mm
scale.
• Your new measurement is 21.70 cm.
• If the measurement was halfway between the 7
mm and the 8 mm marks, your measurement
would be 21.75 cm.
Significant Figures (sig figs) Rules
1.
2.
All non-zero digits are significant.
In whole numbers that end in zero,
the zeros at the end are not
significant.
How many sig figs?
•7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000
•1
•1
•1
•1
•1
•1
Significant Figures (sig figs) Rules
(cont.)
3.
4.
If zeros are sandwiched between nonzero digits, the zeros become
significant.
If zeros are at the end of a number
that has a decimal, the zeros are
significant. These zeros 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
•
•
•
•
•
•
4
2
5
3
3
6
Adding and Subtracting with
Sig Figs
When adding or subtracting measured
numbers, the answer can have no more
places after the decimal than the LEAST of
the measured numbers.
Examples :
1. 2.45cm + 1.2cm = 3.65cm
Round off to = 3.7cm
2. 7.432cm + 2cm = 9.432 round to  9cm
Multiplying and Dividing
with Sig Figs
When multiplying or dividing, the result
can have no more significant figures than
the least reliable measurement.
Examples:
1. 56.78 cm x 2.45cm = 139.111 cm2
Round to  139cm2
2. 75.8cm x 9.6cm = ?