Significant Figure Rules
- the precision of measurements are indicated
based on the number of digits reported.
- Significant figures are the digits that are reported.
Rules:
1. Non-zero digits (1,2,3,4,5,6,7,8,9) are always
significant.
2. Any zeros between two significant digits are
significant. (ex. 103 = 3 sig figs, 12.06 = 4 sig
figs, 100 = 1 sig fig)
3. A final zero or trailing zeros in the decimal
portion ONLY are significant.
a. In other words: zeros after the number past
the decimal are significant (ex. 8.20 = 3 sig
figs)
b. Zeros before the number past the decimal
are place holders – not significant (ex. .002 =
1 sig fig, 2.002 = 4 sig figs)
Examples for you to try. How many sig figs?
a.) 35 g
b.) 3.57 m
c.) 3.507 km
d.) 0.035 kg
e.) 0.246 L
f.) 0.004 m2
g.) 24.068 kPa
h.) 268 K
i.) 20.04080 g
j.) 730000
k.) 6.751
l.) 0.070
Scientific Notation
4,800,000,000 M = 4.8 x 109 M
- move the decimal to the right, increase the
exponent, making it more positive. The decimal has
to be between the first and second number.
.000000048 M = 4.8 x 10-8
- move the decimal to the left, decrease the
exponent, making it more negative. The decimal
has to be between the first and second number.
When adding and subtracting scientific notation,
be sure exponents are the same.
Adding: 2.3 x 104 + 4.6 x 105
= 46 x 104
+
2.3 x 104
46.0 x 104
48.3 x 104 = 4.83 x 105
Subtracting: 3.2 x 108 – 1.1 x 107
-
3.2 x 108
.11 x 108
9.09 x 108
Another Example:
Be sure exponents are the same!
15.6 x 106 + 1.65 x 108
15.6 x 106 + 165.0 x 106 = 180.6 x 106 = 1.806 x 108
Multiplying: Add Exponents
(2 x 103) x (3 x 102) = 6 x 105