Significant Figures
Types of Numbers
Three different types of numbers
• Counting
– Numbers without units (whole numbers)
– Ex: there are 6 chairs in the front row
• Measured
– Numbers WITH units (actually measured)
– Ex: 58.35 g
• Defined
– Fractions or conversion factors
– Ex: 12 inches = 1 foot, 2.54 cm = 1 inch
Determine the type of #
•
•
•
•
12 people
•
5.34 g
•
16 Tbsp in a cup •
6 cans
•
16 oz in a pound
2.54 cm in an inch
40.75 in
2.25 cm
Determine the type of #
•
•
•
•
12 people
•
5.34 g
•
16 Tbsp in a cup •
6 cans
•
16 oz in a pound
2.54 cm in an inch
40.75 in
2.25 cm
Determine the type of #
•
•
•
•
12 people
•
5.34 g
•
16 Tbsp in a cup •
6 cans
•
16 oz in a pound
2.54 cm in an inch
40.75 in
2.25 cm
Determine the type of #
The highlighted are
DEFINED NUMBERS
•
•
•
•
12 people
•
5.34 g
•
16 Tbsp in a cup •
6 cans
•
16 oz in a pound
2.54 cm in an inch
40.75 in
2.25 cm
SF in numbers
• Counting – infinite, ∞
• Defined – infinite, ∞
• Measured – (where the fun begins!
– Digits 1 – 9 ALWAYS count
)
SF for measured #
• Zeros SOMETIMES count
– LEADING zeros NEVER COUNT
• 0234
• 0.00234
3 SF
3 SF
– MIDDLE zeros ALWAYS COUNT
• 101
• 5.01
3 SF
3 SF
SF for measured #
CONT
– TRAILING zeros count if a decimal is
present
• 100.0
• 0.900
• 100
4 SF
3 SF
1 SF
Determine type of ZERO, then # SF
A. 0.031 or 3.1*10-2cm
B. 6.00 cm
C. 107.05 cm
D. 2.35*10-3g
E. 12.05 mL
F. 0.14 cm
G. 3.01 cm
H. 5.790 g
A. Leading, 2
B. Trailing, 3
C. Middle, 5
D. Leading, 3
E. Middle, 4
F. Leading, 2
G. Middle, 3
H. Trailing, 4
SF in Calculations
•Addition and subtraction
-Least number of decimal places
12.0 cm
+2.45 cm
14.45 cm
Round to tenth
14.5 cm
5.79 g
-3.2 g
2.59 g
Round to tenth
2.6 g
SF in Calculations CONT
• Multiplication and division
– Least number of SF
122.5 g
6 cm
*6 cm
2.0 g/mL
36 cm2
= 61.25 mL
Round to 1 SF
Round to 2 SF
2
40 cm
61 mL
Homework
• Complete SF worksheet
• Work on next set of elements