Foundations of Engineering

1. FOUNDATIONS OF
ENGINEERING

2. CHAPTER # 7
Numbers

3. NUMBER NOTATIONS
U.S. standard decimal notation 4,378.1
European standard decimal notation 4.378,1
Acceptable conversion 4378.1
Some number are much larger & smaller to be written in scientific notation
E.g. 602,213,670,000,000,000,000,000
6.0221367 x 10^24
0.60221367 x 10^24
.593 -> Popular press notation -> >1 nos.
0.593 -> Engineering notation

4. SIMPLE ERROR ANALYSIS
-> Examples
Counting marbles (Exact)
Measuring length of rod (Continuous)
 Between 7 & 8 –> length is 7.5 +/- 0.5cm
 Between 7.5 & 7.8 -> length is 7.55 +/- 0.05cm
 Between 7.57 & 7.59 -> length is 7.58 +/- 0.01cm
Exact solution is possible by Micrometer or Lasers.
Integers are exactly by computer up to some limit but the real numbers is represented by
floating point value.

5. SOME TERMINALOGIES
Accuracy: The extent to which the reported value approaches to “true” value & is free from
error.
Precision: The extent to which the measurement may be repeated and the same answer is
obtained
Random errors: Results from many sources, such as random noise in electric circuits &
inability to reproducibly read instruments
Systematic errors: Results from a measurement method that is inherently wrong
Uncertainty: Results from random errors & shows lack of precision
Fractional Uncertainty = Uncertainty/ Best Value
Percent Uncertainty = (Uncertainty/ Best Value) x 100 %
Error: Reported value –True Value
Fractional Uncertainty = Error/ True Value
Percent Uncertainty = (Error/ True Value) x 100 %

6. SIGNIFICANT FIGURES
How many Significant Figures should I used when reporting a number?
RULES TO BE FOLLOWED
A significant figure is an accurate digit, although the last digit is accepted to have some error
The number of significant figures does not includes the zeros required to place the decimal points
It is impossible to determine whether the last zero is truly significant, or whether it is
needed to locate the decimal place. To avoid this we use Scientific Notation.
Infinite zeros
Rounded Figures
Numbers resulting from mathematical relationships
Rounded Error: Rounded should always have to be perform at the end. If not it is
called Rounded Error

7. Significant Figures:
Multiplication/ Division A x B = C
Addition/ Subtraction A + B = C