Download Rules for Counting Significant Figures

Rules for Counting Significant Figures
1.
Nonzero Integers.
Nonzero integers always count as significant figures.
Ex:
Ex:
2.
The number 72,555 has 5 significant figures.
The number 343 has 3 significant figures.
Zeros. There are three classes of zeros:
a.
Leading zeros are zeros that precede all the nonzero digits. These do not
count as significant figures.
Ex:
Ex:
b.
Captive zeros are zeros between nonzero digits. These always count as
significant figures.
Ex:
Ex:
c.
The number 905, has 3 significant figures.
The number 64,004 has 5 significant figures.
Trailing zeros are zeros at the right end of the number. They are
significant only if the number contains a decimal point. Often times a line
is placed over the last zero that is significant if a decimal point is not used.
Ex:
Ex:
Ex:
Ex:
d.
The number .00092 has only 2 significant figures.
The number 0.0345 has only 3 significant figures.
The number 7,000 has only 1 significant figure.
The number .00350 has 3 significant figures.
The number 200. has 3 significant figures.
The number 12,000 has 4 significant figures.
Exact numbers. Many times calculations involve numbers that were not
obtained using measuring devices but were determined by counting.
Ex:
18 students, 8 apples, 356 molecules
Such numbers are called exact numbers. They can be assumed to have an
infinite number of significant figures. Often times they are part of an
equation.
Ex:
circumference = 2r where 2 is an exact number
Exact numbers also can arise from definitions.
Ex:
1 inch = 2.54cm This is a definition so both numbers are exact.
Rules for Rounding
1.
If the digit to be removed
a.
is less than 5, the preceding digit stays the same.
Ex:
b.
is equal to or greater than 5, the preceding digit is increased by 1.
Ex:
2.
1.33 rounds to 1.3
1.36 rounds to 1.4,
3.15 rounds to 3.2
When rounding off, use only the first number to the right of the last significant
figure.
Rules for Using Significant Figures in Calculations
1.
2.
For multiplication or division, the number of significant figures in the result is the
same as that in the measurement with the smallest number of significant figures.
We say this measurement is limiting, because it limits the number of significant
figures in the result.
Ex:
4.56 x 1.4 = 6.38
which is rounded to 6.4 because 1.4 has only 2
significant figures.
Ex:
8.315  298 = .0279027
which is rounded to .0279 because 298 has
3 significant figures
For addition or subtraction, the limiting term is the number that has the leftmost
estimated digit. Round the final answer to the place value of this estimated digit.
If all number have decimal values the limiting term is the one with the smallest
number of decimal places.
Ex:
12.11 + 18.0 + 1.013 = 31.123
which is rounded to 31.1 b/c 18.0 has
only one decimal place