CHEM 11111
Calculations in Chemistry
Dr. S. Sri Skandaraja
Department of Chemistry
University of Kelaniya
Rules for counting significant figures
 Zeros within a number are always significant.
– Both 4308 and 40.05 contain four significant figures.
 Zeros that do nothing but set the decimal point are not
significant.
– Thus, 470,000 has two significant figures.
 Trailing zeros that aren't needed to hold the decimal point are
significant.
– For example, 4.00 has three significant figures.
– 40. has two significant figures.
 Zeroes before a number do not count as significant figures.
– The number 0.004 has one significant figure.
 Exact numbers and constants need not be considered when
counting significant figures.
Significant figures are one way of
expressing uncertainty in
measurements.
1234
500
500.
13000
2.000
101.001
41003
significant figure: The number
of significant digits in a quantity
is the minimum number of digits
needed to express the quantity in
scientific notation..
Adding and subtracting with sig figs:
Keep least sig figs beyond the decimal point
121.795
Adding and subtracting with sig figs:
Keep least sig figs beyond the decimal point
WATCH OUT:
SAME POWERS OF 10!
Multiplying and dividing with sig figs:
Keep least sig figs.
logarithms with sig figs:
sig figs. in mantissa = sig figs in number
log(3.39 x 102) =
log(3.39) + log (102) =
0.530 + 2 = 2.530
log(3.39 x 10-5) =
log(3.39) + log (10-5) =
0.530 – 5 = -4.470
NB 1 sig fig!
Propagation of Uncertainty
from Random Error
The volume delivered by a buret is the difference between final
and initial readings. If the uncertainty in each reading is 0.02 mL,
what is the uncertainty in the volume delivered?
Suppose that the initial reading is 0.05 (±0.02) mL and the
final reading is 17.88 (±0.02) mL. The volume delivered is the
difference:
Regardless of the initial and final readings, if the
uncertainty in each one is ±0.02 mL, the uncertainty in
volume delivered is ±0.03 mL.
What would be the uncertainty in volume delivered if the
uncertainty in each reading were 0.03 mL? (Answer: 0.04 mL)
Propagation of Uncertainty
from Random Error
= 5.64 ± 0.23