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BRCC
CHM 101
Handout
Chapter 1
Page 1 of 2
Significant Figures
“ Every measurement has a degree of uncertainty.
For example, a buret can deliver a volume of liquid 8.00 +/- .01 mL. Instead of
using “+/-” it is understood that there is an uncertainty of at least one unit in the last
digit. You simply write 8.00.
Significant figures - are the meaningful digits obtained in a measurement.
How do you count significant figures?
1.
All nonzero digits are significant.
5.37 cm has 3 significant figures
2.
Zeros between nonzero digits are significant.
1.04 g has 3 significant figures
3.
Zeros beyond the decimal point at the end of
a number are significant.
8.00 mL has 3 significant figures
4.
Zeros preceding the first nonzero digit in a
number are not significant.
0.005 has 1 significant figure
“ It is best to express numbers in exponential or scientific notation to avoid being
ambiguous.
0.005 become 5 x 10-3 in scientific notation.
How many significant figures are in the number 500? You can’t tell unless you use
scientific notation.
5.00 x 102 has 3 significant figures
2
5.0 x 10 has 2 significant figures
5
x 102 has 1 significant figure
Calculating with significant figures
Multiplication and Division - when multiplying or dividing, the number of significant
figures in the answer is the same as the quantity with the smallest number of significant
figures. You must sometimes round off.
5.27 x 2.1 = 11 (2 significant figures)
64.08 ÷ 12.2 = 5.25 (3 significant figures)
BRCC
CHM 101
Handout
Chapter 1
Page 2 of 2
Rules for rounding:
1.
If the digits to discard are less than “500" as in the number 23.489, leave the last
digit unchanged. The number 23.489 rounded to 2 significant figures becomes 23.
2.
If the digits to discard are greater than “500" as in the number 23.624, round the
last digit up. The number 23.624 rounded to 2 significant figures becomes 24.
3.
If the digits to discard are “500" as in the number 23.500, the book says to round
off so that the last digit is an even number. This means that 23.500 and 24.500
both round to 24. However, most people have been taught to round up in this
situation. If you round up, you will not be penalized.
Addition and Subtraction - the sum or difference should be rounded off to the same
number of decimal places as there are in the quantity with least number of decimal
places.
22.610 g { 3 places past the decimal }
5.7 g { 1 place past the decimal }
+ 17.44 g { 2 places past the decimal }
-----------------45.8 g
Exact Numbers: Exact numbers are not measured quantities. You find exact number
in formulas for example.
“
You use the concept of significant figures with measured quantities only.
In the equation
°F = 1.8 x °C + 32°
1.8 and 32 are exact quantities.