AdjustmentSome survey processes are not complete untilmeasurements are within usable limits or untilcorrections have been applied to these measure-ments to distribute accumulated errors. Smallerrors that are not apparent in individual measure-ments can accumulate to a sizeable amount.Adjusting is the process used to distribute theseerrors among the many points or stations untilthe effect on each point has been reduced to thedegree that all measurements are within usablelimits.For example, assume that 100 measurementswere made to the nearest unit for the accuracyrequired. This requires estimating the nearestone-half unit during measurement. At the end ofthe course, an error of + 4 units results. Adjustingthis means each measurement is reduced 0.04 unit.Since the measurements were read only to thenearest unit, this adjustment would not bemeasurable at any point, and the adjusted resultwould be correct.SIGNIFICANT FIGURES.— The term signif-icant figures refers to those digits in a number thathave meaning; that is, whose values are definitelyknown to be exact.In a measured quantity, the number ofsignificant figures is determined by the accuracyof the measurement. For example, a roughlymeasured distance of 193 ft has three significantfigures. More carefully measured, the samedistance, 192.7 ft, has four significant figures. Ifmeasured still more accurately, 192.68 ft has fivesignificant figures.In surveying, the significant figures shouldreflect the allowable error or tolerance in themeasurements. For example, suppose a measure-ment of 941.26 units is made with a probable errorof ± 0.03 unit. The ± 0.03 casts some doubt onthe fifth digit which can vary from 3 to 9, but thefourth digit will still remain 2. We can say that941.26 has five significant figures; and from theallowable error, we know the fifth digit isdoubtful. However, if the probable error were±0.07, the fourth digit could be affected. Thenumber could vary from 941.19 to 941.33, andthe fourth digit could be read 1, 2, or 3. The fifthdigit in this measurement is meaningless. Thenumber has only four significant figures andshould be written as such.The number of significant figures in a numberending in one or more zeros is unknown unlessmore information is given. The zeros may havebeen added to show the location of the decimalpoint; for example, 73200 may have three, four,or five significant figures, depending on whetherthe true value is accurate to 100, 10, or 1 unit(s).If the number is written 73200.0, it indicatesaccuracy is carried to the tenth of a unit and isconsidered to have six significant figures.When decimals are used, the number ofsignificant figures is not always the number ofdigits. A zero may or may not be significant,depending on its position with respect to thedecimal and the digits. As mentioned above, zerosmay have been added to show the position of thedecimal point. Study the following examples:0.000047 . . . . . . .0.0100470 . . . . . . .0.1000470 . . . . . . .2.0100470 . . . . . . .two significant figuressix significant figuresseven significant figureseight significant figuresIn long computations, the values are carriedout to one more digit than required in the result.The number is rounded off to the requirednumbers of digits as a final step.ROUNDING OFF NUMBERS.— Roundingoff is the process of dropping one or more digitsand replacing them with zeros, if necessary, toindicate the number of significant figures.Numbers used in surveying are rounded offaccording to the following rules:1. When the digit to be dropped is less than5, the number is written without the digit or anyothers that follow it. (Example: 0.054 becomes0.05.)2. When the digit is equal to 5, the nearestEVEN number is substituted for the precedingdigit. (Examples: 0.055 becomes 0.06; 0.045becomes 0.04.)3. When the digit to be dropped is greaterthan 5, the preceding digit is increased by one.(Example: 0.047 becomes 0.05.)4. Dropped digits to the left of the decimalpoint are replaced by zeros.5. Dropped digits to the right of the decimalpoints are never replaced.11-8
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