### Significant Figures

```Rule for Using Sig Figs
in Math:
The result of your calculations can
never be more precise than your
LEAST precise number!
Example
 You
may know very precisely that the
volume of your bucket is 401234.2 ml , but
if you have a very uncertain number of
drops/ml (24 drops/ml)…
24 drops/ml x 401234.2 ml =
9629620.8 drops?
-or9600000 drops?
Multiplication/Division

Round to the same number of places as the
number with the least sig figs.
 12 x 230.1 = 2761.2 (calculator) = 2800
 0.00325 / .120 = 0.0270833333333 (calc)
= 0.0271

3.14 45.00
2
= 70.65 (calc)
= 70
 Round
to the last sig fig in the most
uncertain number.
9.12 + 4.3 + 6.01 = ? 19.43 (calc)
9.12
4.3
+ 6.01
19.4
 0.11001
- 2.12 - 12 = ?
-14.00999 (calc)
0.11001
2.12
-12______
-14
3.414 s + 10.02 s + 58.325 s +
0.00098 s
= 71.76 s
1884 kg + 0.94 kg + 1.0 kg
+ 9.778 kg
= 1896 kg
2104.1 m – 463.09 m
= 1641.0 m
2.326 hrs – 0.10408 hrs
= 2.222 hrs
10.19 m x 0.013 m
= 0.13 m2
140.01 cm x 26.042 cm x
0.0159 cm
= 58.0 cm
80.23 m ÷ 2.4 s
= 33 m/s
4.301 kg ÷ 1.9
= 2.3 kg/cm3
3
cm
What if
Multiplication/Division and
combined?
Do it in steps, according to the
order of operations…
(2.39 m – 0.2 m)
12.43 s
=
=
2.2 m
12.43 s
0.18 m/s
2.00 m – 0.500(0 + 3.0 m/s)(3 s)
= 2.00 m – 0.500(3.0 m/s)(3s)
= 2.00 m – 5 m
= -3 m
0.37 m – 1.22 m – (4 m/s)(3.0020 s)
0.5000 x (1.0021s)2
=
0.37m – 1.22m – 10m
0.5000 x (1.0021s)2
=
_____- 10 m______
0.5000 x (1.0021s)2
=
- 20 m/s2
```