Understanding Measurements and Computations: Units, Significant Figures, and Field Notes, Lecture notes of Urbanization

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Measurements and

computations

Contents

• Measurements
• Units of measurement
• Computations
  • Tools for computations
  • Significant figures
  • Rounding off numbers
• Survey Field notekeeping

Measurements

Direct

• Direct comparison with a primary or

secondary standard

• Time  watch
• Mass  beam balance
• Distance  tape, pacing
• Angle  protractor

Measurements

Indirect

• Indirect comparison with a

standard

• Mass  spring balance (expansion)
• Temperature – thermal expansion of mercury
• Distance  travel time of Electromagnetic (EM) or sound waves

Units of measurement

• Distance
  • Imperial units
    • Inch, feet
    • 1 ft = 12 in
  • Metric units
    • metre
    • Metre prefix (kilo, deci, centi, milli)
    • 0.001 km = 1 m = 10 dm = 100 cm = 1000 mm Convert the following
      1. 20 Cape ft. to metres
      2. 20 Eng. ft. to metres

Units of measurement

• Area
  • Square metres
  • Square foot
  • Hectare
  • Acre
  • Morgen Convert the following
    1. 8 acres to sq. metres
    2. 8 Ha to sq. metres
    3. 10 acres to Ha

Tools for computing

• Calculators
  • Scientific calculators with trigonometric functions (direct and inverse)
  • Have memory registers
  • Some are programmable
• Computers
  • Performs computations for data reduction and problem solving
  • Can display images graphically using (CAD and GIS)
    • Examples
      • CAD --- AutoCAD, MicroStation
      • GIS --- QGIS, ArcGIS, MapInfo Ensure that you familiarize yourself with your scientific calculator

Significant Figures

• The number of significant digits in a number/value.
• It is an indication of the accuracy obtained in an observation.
• Measurements can only be accurate to the degree that the measuring

instrument is precise.

• Accuracy of field data cannot be improved by computational

processes

• Multiplication/division
  • The LEAST number of significant figures in any number of the problem determines the number of significant figures in the number. 26. x 10.

x 10.

wrong correct

Rules and conventions :

• All non-zero digits in a number are significant.
  • Example: Numbers 0.0000216, 0.0216, 21.6 and 216 have the same number of significant figures namely three (2, 1, 6).
• All zeros between two non-zero digits are significant, no matter where the decimal point is, if at all. - Example : In the numbers 0.0000206, 0.0206, 20.6 and 206, the zero lying between the digits 2 and 6 is only significant.
• If the number is less than 1, the zeroes on the right of decimal point but to the left of the first non-zero digit are not significant. - Example : In 0.0000206, the four zeros after decimal and before the digit 2 has no significance. Similarly, in 0.0206, the zero after decimal and before the digit 2 has no significance. So the number of significant figures of these numbers are three (2, 0 and 6).

Rounding off

• When doing calculations always give the final answer with the correct

number of decimal places or significant figures by rounding off.

• A computed result with many significant figures implies more

exactness than it is warranted or is even possible to be measured.

Survey Note Keeping

• Field notes
• Importance of field notes
• Types of field notes
• Arrangement of field notes
• Guidelines

Importance of field notes

1. Field notes perpetuate a survey even when stakes have rotted and

monuments are obliterated. They make it possible to re-establish

lost monuments or other measured data.

2. Field notes of cadastral surveys are important documentation in

court cases arising between land authorities and landowners.

3. Field notes are the means of communication between field and

office personnel.

Types of field notes

• Sketch and/or Description notes
  • A sketch is used to clarify information in other types of field notes and avoid misinterpretation.
  • Sketches increase the efficiency with which notes are taken and subsequently interpreted.
  • Description notes are a written narration of the survey procedure and of the measurement to clarify information in other types of notes.