Surveying I– coordinate account

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Principles calculations

In surveying each measurement is made with a specified accuracy. Therefore, the accounts should be able to perform actions on the approximate numbers. The method of calculation of geodesic is contained in the rules below Krylov-Bradisa.

When calculating the indirect results of the account should be taken is always one digit more than is indicated by the following rules.

When adding and subtracting numbers should be rough enough decimal places, if their number includes the smallest number of decimal digits*.

Example

2,44 + 3,2 + 8,9991 = 14,6391≈14,6
Of the three components of the smallest number of decimal digits is the number of 3,2 (in this case it is a decimal digit), so the outcome will be accurate to one decimal place.

When multiplication and division should save as much as a result of significant figures **, provided it includes the approximate number of them with the fewest significant digits.

Example 1

(The color orange has been marked with the number of significant digits)

0,05 : 4000 = 0,0000125≈ 0,00001
As the number of 0,05 has only one significant figure, so the result should be given only one significant figure.

Example 2

(The color orange has been marked with the number of significant digits)

1234 • 0,0102≈12,6
As the number 0,0102 has three significant figures, therefore, as a result should be given only three significant digits.

With increasing numbers of second and third power should be enough to keep as a result of significant figures as their number includes a power series.

Example

(The color orange has been marked with the number of significant digits)

4,5² ≈ 20
The number of 4,5 has two significant figures, therefore, should be also a result of two significant digits.

When calculating the root of second or third degree as a result of the number should be enough significant figures, if contains the number of elements.

Example

(The color orange has been marked with the number of significant digits)

√_____ 0,786= 0,887
The number 0,786 has three significant figures, therefore, should be preserved as a result of the three significant figures.

Note: Even if the next decimal places are all zeros, save them as much as they should be of significant digits.

Example

Counting the coordinates of point P to the nearest millimeter write P (300.000 m 812.400 m). Mistake is to write P (300, 812.4 m).

By making calculations on the approximate numbers also appears the problem of rounding. It should be guided by the following principles:
- the last recorded digit increases by 1 when the first digit discarded is greater than 5;
- the last of the recorded figures is left unchanged, when the first digit discarded is greater than 5;
- if the first digit discarded is 5:
a) and are followed by further digits other than zero, the last of the stored numbers increased by 1;
b) and there are no numbers on it further, then the last digit is left to be saved without change, if it is an even number, and when the odd is increased by 1.

Examples

0,332≈0,3;
2,76≈2,8;
81,256≈81,3;
81,250≈81,2;
497,35≈497,4.

 *The number of Decimal Places – areas located on the right of the decimal point.
**Significant figures the number is called all the numbers except the zeros located on the left of the first digit different from zero. Example: In a number 0,001002, significant digits is: 1002, and in a number 3289 - the significant figures are all the numbers.