FOUNDATIONS OF ENGINEERING

CHAPTER # 7Numbers

NUMBER NOTATIONSU.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

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.

SOME TERMINALOGIESAccuracy: 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 %

SIGNIFICANT FIGURESHow many Significant Figures should I used when reporting a number?

RULES TO BE FOLLOWEDA 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

Significant Figures:Multiplication/ Division A x B = C

Addition/ Subtraction A + B = C