Significant Figures
Goals
To learn to determine the number of significant figures in a number.
To
use significant figures correctly in calculations.
To learn to use scientific notation.
Determining the number of
significant figures (S. F.) in a number
Measure
numbers always contain error. Numbers
obtained by counting or defined numbers are exact. For example 28 students is
exact. 12 inches in one foot is defined
and is also exact. An exact number has
an infinite number of significant figures.
The number of significant figures in a measured number is limited by the
measuring device used
Rules for Counting
Significant Figures: Example # S. F.
1.
All nonzero integers are significant.
421.1 4
2.
Leading zeros are never significant. 0.0034 2
3.
Captive zeros are always significant. 205 3
4.
Trailing zeros in a decimal number are significant. 25.0 3
5.
Trailing zeros in a number with no decimal are not significant. 400 1
Exponential Notation:
The
number of significant figures in a number written in exponential notation is
easily determined as the leading and trailing zeros are removed.
Examples:
Decimal Exponential
notation # S. F.
0.0034 3.4
x 10 ¾ 3 2
400 4
x 10 2 1
0.000505 5.05
x 10 ¾ 4 3
530000 5.3
x 10 5 2
0.0100
1.00
x 10 ¾ 2 3
(0.0100
contains trailing zeros within a decimal.)
Rules for Rounding:
1.
In a calculation carry all
of the significant figures through to the final result, then round.
2.
If the digit to be removed
is <5, the preceding digit remains unchanged. 25.44 rounds to 25.4.
3.
If the digit to be removed
is >= 5, then the preceding digit is incremented by 1. 25.46 rounds to 25.5.
Significant
Figures Worksheet:
Name:_______________________________________________________
1. Determine the number of Significant Figures:
(A)
0.000170
g________________ (B) 102 mm ________________
(C)
2
books ________________ (D) 3800 km ________________
2.
Write in scientific
Notation:
(A) 0.00451 g __________________ (B)
21300 m ________________
3.
Round the following numbers
to:
Three significant Figures Two
significant Figures
(A)
0.005484 _____________________ ____________________
(B)
271.75 _____________________ ____________________
(C)
13469 _____________________ ____________________
4.
Multiplication and Division:
Remember that the calculated answer is rounded off
to the same number of significant figures as the measured number with the fewest
significant figures.
(A) (3.722x10−7) x (2300) =_______________ (B)
_____________
4.
Addition and Subtraction:
Remember that the calculated answer is rounded off
to the same number of significant figures after the decimal as the measured
number with the fewest significant figures after the decimal. The 100 on pt. C is exact.
(A)
2.754
mL − 2.63 mL
= ____________
(B) 7.33x10−2mL− 1.8 x10−4
mL = ____________
(C) 
= _______________
(D) 875 g −50 g = ______________