Transcript sigfig lecture

Significant Figures
when counting, significant numbers are
exact:
# people in this room
# eggs in a carton
# cars in a parking lot
Measurements can also be exact:
My height is 1.740 m,
not 1.739m or
1.741m
Most measured numbers are limited by the
precision of the tool used or the person
using the tool.
Calculations are almost never exact
When using measured numbers in
calculations,
not all the numbers in your answer
count they are
insignificant
KEY CONCEPT: Your answers cannot be
more accurate than the precision of your
instrument.
But, Calculators will often give more digits
than are actually accurate (significant)
often giving insignificant answers:
12.36g / 4.7 cm3 = ?
2.62978723 g/cm3 this number is wrong!!
all the numbers in blue are insignificant
and cannot be used
Why?
Rules for sigfigs:
1. Answer cannot be more accurate than the least
accurate number used to calculate it (airplane effect)
2. Digits 1 through 9 are significant:
258 = 3 sigfigs, 13,967 = 5sf, 0.00245 = 3sf
3. Zeros between other sigfigs are significant (oreo
effect):
4903 = 4sf, 298006 = 6sf, 0.00 2045 = 4sf
4. For numbers > 1, zeros to the right of decimal are
significant (they indicate measured values), thus
show accuracy:
387.00 = 5 sf, 24.0000 = 6 sf
5. for whole numbers > 1 but without a
decimal, the last zeros are insignificant:
210
: 2 sigfigs
32,500 : 3 sig figs
210.
: 3 sigfigs
32,500. : 5 sigfigs
6. For numbers <1, zeros between the decimal
point and the first significant number are
insignificant (false oreo):
0.00536 = 3sf, 0.000000004 =1sf
7. For numbers <1, zeros to the left of the
decimal are insignificant (signal decimal
coming):
0.00536 =3sf, 0.000000004 =1sf
8. For numbers with decimals, zeros to the right
of a significant digit are significant:
0.00340 = 3sf, 0.000010 = 2sf, 345.010 = 6sf
9. Follow the rounding rules to obtain proper
sigfigs:
<5 round down: 2.34 = 2.3
>5 round up: 5.68 = 5.7
10. When calculating, answers are only
accurate to the least accurate number
used:
25 / 2.35 = 10.63829787
= 11
34.3 / 64 = 0.5359375
= 0.54
2.13 x 0.15 = 0.32
Examples:
#
#sigfigs
1.24
3
16.3
3
52.0
3
250.
3
0.32
2
0.510
3
0.021
2
0.00353 3
1,001
4
How many sif figs?
1070
139
1390
1390.
1390.0
1390.011
0.019
0.0190
0.01901
0.019010
All calculations for the rest of this year MUST be
in sigfigs!!!!!!
Quick rule of thumb for sigfigs:
Any number w/ a decimal point:
-moving from left to right
-once you hit a # 1-9, all numbers and zeros
are significant
105.030 = 6 sf
0.0003029 = 4 sf