Some survey processes are not complete until
measurements are within usable limits or until
corrections have been applied to these measure-
ments to distribute accumulated errors. Small
errors that are not apparent in individual measure-
ments can accumulate to a sizeable amount.
Adjusting is the process used to distribute these
errors among the many points or stations until
the effect on each point has been reduced to the
degree that all measurements are within usable
For example, assume that 100 measurements
were made to the nearest unit for the accuracy
required. This requires estimating the nearest
one-half unit during measurement. At the end of
the course, an error of + 4 units results. Adjusting
this means each measurement is reduced 0.04 unit.
Since the measurements were read only to the
nearest unit, this adjustment would not be
measurable at any point, and the adjusted result
would be correct.
SIGNIFICANT FIGURES. The term signif-
icant figures refers to those digits in a number that
have meaning; that is, whose values are definitely
known to be exact.
In a measured quantity, the number of
significant figures is determined by the accuracy
of the measurement. For example, a roughly
measured distance of 193 ft has three significant
figures. More carefully measured, the same
distance, 192.7 ft, has four significant figures. If
measured still more accurately, 192.68 ft has five
In surveying, the significant figures should
reflect the allowable error or tolerance in the
measurements. For example, suppose a measure-
ment of 941.26 units is made with a probable error
of ± 0.03 unit. The ± 0.03 casts some doubt on
the fifth digit which can vary from 3 to 9, but the
fourth digit will still remain 2. We can say that
941.26 has five significant figures; and from the
allowable error, we know the fifth digit is
doubtful. However, if the probable error were
±0.07, the fourth digit could be affected. The
number could vary from 941.19 to 941.33, and
the fourth digit could be read 1, 2, or 3. The fifth
digit in this measurement is meaningless. The
number has only four significant figures and
should be written as such.
The number of significant figures in a number
ending in one or more zeros is unknown unless
more information is given. The zeros may have
been added to show the location of the decimal
point; for example, 73200 may have three, four,
or five significant figures, depending on whether
the true value is accurate to 100, 10, or 1 unit(s).
If the number is written 73200.0, it indicates
accuracy is carried to the tenth of a unit and is
considered to have six significant figures.
When decimals are used, the number of
significant figures is not always the number of
digits. A zero may or may not be significant,
depending on its position with respect to the
decimal and the digits. As mentioned above, zeros
may have been added to show the position of the
decimal point. Study the following examples:
0.000047 . . . . . . .
0.0100470 . . . . . . .
0.1000470 . . . . . . .
2.0100470 . . . . . . .
two significant figures
six significant figures
seven significant figures
eight significant figures
In long computations, the values are carried
out to one more digit than required in the result.
The number is rounded off to the required
numbers of digits as a final step.
ROUNDING OFF NUMBERS. Rounding
off is the process of dropping one or more digits
and replacing them with zeros, if necessary, to
indicate the number of significant figures.
Numbers used in surveying are rounded off
according to the following rules:
1. When the digit to be dropped is less than
5, the number is written without the digit or any
others that follow it. (Example: 0.054 becomes
2. When the digit is equal to 5, the nearest
EVEN number is substituted for the preceding
digit. (Examples: 0.055 becomes 0.06; 0.045
3. When the digit to be dropped is greater
than 5, the preceding digit is increased by one.
(Example: 0.047 becomes 0.05.)
4. Dropped digits to the left of the decimal
point are replaced by zeros.
5. Dropped digits to the right of the decimal
points are never replaced.