# Calculations with Significant Figures Rules for Counting Significant Figures

```Calculations with Significant Figures
Rules for Counting Significant Figures
Rules for Significant Figures in Calculations
For Multiplication and Division
a. Count the number of significant figures in each measurement
c. Round the result so it has the same number of significant figures as the
measurement with the smallest number of significant figures
4.5 cm
x
2 sig figs
0.200 cm
3 sig figs
=
0.90 cm2
2 sig figs
a. Result is limited by the number with the smallest number of
significant decimal places
b. Find last significant figure in each measurement
c. Find which one is “left-most”
d. Round answer to the same decimal place
450 mL
+
precise to 10’s place
27.5 mL
=
480 mL
precise to 0.1’s place
precise to 10’s place
Rules for Rounding Off
1. If the digit to be removed is:
a. &lt; 5, the preceding digit stays the same (1.33 becomes 1.3)
b. ≥ 5, the preceding digit is increased by 1 (1.36 becomes 1.4)
In a series of calculations, carry the extra digits to the final result and then
round off.
1.5 x 2.54 = 3.81 &divide; 2.33 = 1.6351931 Rounds to 1.6
Don’t forget to add place-holding zeros if necessary to keep value the same!!
3.496 (4 figs) rounds to 3.50 (3 sig figs) not 3.5 (2 sig figs)
I.
Density
A.
Density is a property of matter representing the mass per unit volume d = m/V
1. Density can be used to identify unknowns or test for composition
2. Density : solids &gt; liquids &gt;&gt;&gt; gases
3. Solids = g/cm3
Liquids = g/ml
Gases = g/L
4. Example 25.00 ml of isopropanol = 19.625 g d = ?
d = 19.624g / 25.00 ml = 0.7850 g/ml
5. Today: Identify metal based on its density
a) Measure mass of unknown metal object on balance
b) “Tare” sets the balance to 0.000 g
c) Measure mass to 0.001 g
d) Volume of object by displacement of water in graduated cylinder
Vobject = V(water + object) – V(water only)
mass( g )
d
volume(cm3 )
Al = 2.70 g/cm3
Brass = 8.40 g/cm3
% Error 
d ex  d known
d known
Fe = 7.87 g/cm3
Pb = 11.34 g/cm3
x100%
II.
Graphing
A.
Circumference = Pi x Diameter (C = pd) (y = mx + b)
1. Measure C and d for several different sizes of beakers
2. diameter (cm)
circumference (cm)
10
31
20
63
30
94
40
123
3. Manual Graph
a. Required: Title, Name, Date, Axes Labels with units,
use most of paper
b. Best fit straight line
rise y y2  y1
c.
Slope 
4.
B.
run

x

x2  x1