SIGNIFICANT FIGURES
• Measured Data
• Counted & Defined Data (exact numbers)
• Calculated Data
– Multiplication & Division
– Addition & Subtraction
Significant Figures
• All the certain digits plus one uncertain
digit.
X.XXX . . . .
X.XXX . . . .
We Need Some Rules!!!
The 5 Rules
• All non-zero digits are significant.
• Zeros at the beginning of a number are not
significant.
• Zeros to the right of a decimal point are significant
IF they are preceded – anywhere in the number –
by significant digits.
• Zeros between significant digits are significant.
• If a number ends in zeros and a decimal point is
not shown, the number of significant figures is
indeterminate.
Some Examples
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1.2 m
1.25 m
0.0027 g
6.000 m
10.002 g
0.0050 g
50.0500 g
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2 SF
3 SF
2 SF
4 SF
5 SF
2 SF
6 SF
More Examples
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100 mm
10.0 cm
1000 mL
1000. mL
1000.0 mL
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Indeterminate SF
3 SF
Indeterminate SF
4 SF
5 SF
1000 mL written so it has
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1 SF
2 SF
3 SF
4 SF
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1 x 103 mL
1.0 x 103 mL
1.00 x 103 mL
1.000 x 103mL
Counted Data
• There were 15 cars in the parking lot.
– Number is really 15.00000 . . . .
• Number of significant figures is infinite
• There were 20 students in the classroom
– Number is really 20.00000 . . . .
• Number of significant figures is infinite
Defined Data
• There are 12 inches in a foot
– Number is really 12.00000 . . . .
• Number of significant figures is infinite
• There are 100 centimeters in a meter
– Number is really 100.00000 . . . .
• Number of significant figures is infinite
More Examples
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22.7 g
100 people
100 mL
100 cm in a m
10.0 s
10. mm
15 pennies
3 feet in a yard
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3 SF
Infinite SF
Indeterminate SF
Infinite SF
3 SF
2 SF
Infinite SF
Infinite SF
Sig Figs in Calculations
Multiplication & Division
Uncertainty in Calculated Area
• 11.22 m (4.23 m) =
47.4606 m2
• 11.21 m ( 4.22 m) =
47.3062 m2
• 11.20 m (4.21 m) =
47.152 m2
Rule for Multiplication / Division
• The answer can only have as many
significant figures as the number with the
fewest significant figures.
• 11.21 m (4.22 m) = 47.3 m2
• 4 SF ( 3 SF ) = 3 SF
Sig Figs in Calculations
Addition & Subtraction
Uncertainty in Total Length
Rule for Addition / Subtraction
• The answer can only have as many decimal
places as the number with the fewest
decimal places.
• 1.147 m + 15.2 m = 16.3 m
• 3 DP + 1 DP = 1 DP
Mixed Arithmetic