Scientific Notation
• Converting into Sci. Notation:
– Move decimal until there’s 1 digit to its left.
Places moved = exponent.
– Large # (>1)  positive exponent
Small # (<1)  negative exponent
– Only include sig figs.
65,000 kg  6.5 × 104 kg
Scientific Notation
Practice Problems
1.
2,400,000 g
2.4  106 g
2.
0.00256 kg
2.56  10-3 kg
3.
7  10-5 km
0.00007 km
4. 6.2  104 mm
62,000 mm
Calculating with Scientific Notation
Example:
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Chemistry Math
Accuracy and Precision
Percent Error
Significant Figures
A. Accuracy vs. Precision
• Accuracy – a measure of how close a
measurement comes to the true value
• Precision – a measure of how close a
series of measurements are to one
another.
ACCURATE = CORRECT
PRECISE = CONSISTENT
Example:
Low accuracy –
high precision
High accuracy –
low precision
High accuracy –
high precision
B. Calculating Percent Error
• Error – the difference between the
experimental value and the accepted
value.
% error 
experiment
al  accepted
accepted
your value
true value
 100
B. Percent Error
• A student determines the density of a
substance to be 1.40 g/mL. Find the
error and the % error if the accepted
value of the density is 1.36 g/mL.
SIGNIFICANT FIGURES
A New Way To Count
Numbers
C. Significant Figures
• Indicates the precision of a measurement.
• Recording Sig Figs
– Sig figs in a measurement include the known
digits plus a final estimated digit
2.35 cm
2.83 cm
4.50 cm
28.5 ooCC 30.0 mL 4.29 mL
15.0
C. Significant Figures
• Counting Sig Figs
–Count all numbers
EXCEPT:
»Leading zeros -- 0.0025
»Trailing zeros without
a decimal point -- 2,500
C. Significant Figures
Counting Sig Fig Examples
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
C. Significant Figures
• Calculating with Sig Figs
– Add/Subtract - The # with the lowest
decimal value determines the place of the
last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
224 g
+ 130 g
354 g  350 g
C. Significant Figures
• Calculating with Sig Figs
– Multiply/Divide - The # with the fewest sig
figs determines the # of sig figs in the
answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g
EXACT NUMBERS
1. Exact numbers have infinite number of
significant figures. Exact numbers include
1. Counting of anything : 22 people or 10
meter sticks, 6 eggs etc.
2. Defined quantities : 12 = 1 doz.
2. Exact numbers do not affect the rounding to
the correct number of significant figures or
in the calculations of the measurements.
C. Significant Figures
Practice Problems
1. (15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
2. 18.9 g
- 0.84 g
18.06 g  18.1 g
Practice Problems (pg. 70 &71).
• 3). 61.2 meters + 9.35 meters + 8.6 meters =
• 4). 8.3 meters x 2.22 meters=
• 5). 8.345 g / 10.6 mL =