ENGR 107 – Introduction to Engineering
Estimation,
Accuracy and Precision,
and
Significant Figures
(Lecture #3)
ENGR 107 - Introduction to Engineering
1
Estimation
ENGR 107 - Introduction to Engineering
2
Estimation
A rough calculation, often using incomplete or
uncertain data, that is still close enough to be
useful.
Definition courtesy of Wikipedia
Synonym: approximation
ENGR 107 - Introduction to Engineering
3
Estimation


Estimations are used when

Insufficient information is available

Available information is uncertain

Problem is too difficult to solve analytically

Problem is impossible to solve using
available analysis tools.
Estimations are used when

An inexact result is useful

A range (i.e. upper and lower bounds) is
useful ENGR 107 - Introduction to Engineering
4
Estimation
Exercise:
Calculate the volume of a box to the nearest
cubic meter.
The dimensions of the box are:
W = 3.75 m
L = 1.675 m
H = 2.35 m
ENGR 107 - Introduction to Engineering
5
Estimation
Exercise:
Calculate the density of a material to the
nearest kg / m3.
The mass and volume of the material are:
Mass = 489.54 kg
Volume = 7.5 m3
ENGR 107 - Introduction to Engineering
6
Estimation
Exercise:
Determine the number of tiles, to the nearest
integer number, needed to tile a wall.
Dimensions of the tile: 4.5 in. x 4.5 in.
Dimensions of the wall: 7.5 ft. x 11 ft.
ENGR 107 - Introduction to Engineering
7
Estimation
Calculate the volume of the classroom, using
your height as a “measuring stick”.
ENGR 107 - Introduction to Engineering
8
Accuracy and Precision
ENGR 107 - Introduction to Engineering
9
Accuracy and Precision
In measurements, accuracy and precision
have different meanings and cannot be used
interchangeably.
ENGR 107 - Introduction to Engineering
10
Accuracy
The degree of closeness of a measurement to
the actual or true value.
Definition courtesy of Wikipedia
ENGR 107 - Introduction to Engineering
11
Precision
The degree to which repeated measurements
under unchanged conditions show the same
results.
Definition courtesy of Wikipedia
Also called reproducibility or repeatability.
ENGR 107 - Introduction to Engineering
12
Accuracy vs Precision
Accurate
ENGR 107 - Introduction to Engineering
13
Accuracy vs Precision
Precise
ENGR 107 - Introduction to Engineering
14
Accuracy vs Precision
Accurate and Precise
ENGR 107 - Introduction to Engineering
15
Accuracy vs Precision
ENGR 107 - Introduction to Engineering
16
Measurements
ENGR 107 - Introduction to Engineering
17
Measurements


Engineers must be able to measure physical
quantities and express these measurements in
numerical form.
Engineers must have confidence that the
measurements and subsequent calculations and
decisions made based on the measurements are
reasonable.
ENGR 107 - Introduction to Engineering
18
Measurements



Any physical measurement that is not a
countable number will be approximate.
Errors are likely to be present regardless of the
precautions used when making the
measurements.
Significant digits are used to express,
numerically, the accuracy of a measurement.
ENGR 107 - Introduction to Engineering
19
Measurement Estimation



There is a finite accuracy to which every
engineering measurement can be made.
There is a limited number of significant digits
that can be included in the numerical
representation of a measurement.
The engineer must estimate the measurement
between the smallest graduations on the
instrument.
ENGR 107 - Introduction to Engineering
20
Measurement Estimation
ENGR 107 - Introduction to Engineering
21
Errors
ENGR 107 - Introduction to Engineering
22
Errors


Systematic

A bias in the measurement leading to the mean of a set
of measurements differing significantly from the
expected value.

Can be identified and eliminated
Random

An error in the measurement leading to inconsistent
values for repeated measurements of the same attribute.

Caused by unpredictable fluctuations in the readings of
the measurement equipment, in the environment, etc.

Cannot be eliminated
ENGR 107 - Introduction to Engineering
23
Significant Digits
ENGR 107 - Introduction to Engineering
24
Numerical Values



For numbers less than one, a zero is written in
front of the decimal point.
A space, not a comma, is used to divide
numbers of three orders of magnitude or more.
For very large or very small numbers, use
scientific notation to reduce the unwieldy
nature of these numbers.
ENGR 107 - Introduction to Engineering
25
Significant Digits
A significant digit, or significant figure, is
defined as any digit used in writing a number,
except those zeros that are used only for
location of the decimal point or those zeros
that do not have any nonzero digit to their left.
ENGR 107 - Introduction to Engineering
26
Significant Digits


Numbers 10 or larger that are not written in
scientific notation and that are not counts (exact
values) can cause difficulties in interpretation
when zeros are present.
If uncertainty results from using standard
decimal notation, use scientific notation so that
the reader will clearly understand your intent.
ENGR 107 - Introduction to Engineering
27
Significant Digits
ENGR 107 - Introduction to Engineering
28
Significant Digits
Rounding:
Increase the last digit retained by 1 if the first
digit dropped is greater than 5.
ENGR 107 - Introduction to Engineering
29
Significant Digits
Multiplication and Division:
The product or quotient should contain the
same number of significant digits as the
number with the fewest significant digits.
ENGR 107 - Introduction to Engineering
30
Significant Digits
Addition and Subtraction:
The sum or difference should include
significant digits only as far to the right as in
the least precise number.
ENGR 107 - Introduction to Engineering
31
Arithmetic and Significant Digits


In calculator or computer applications it is not
practical to perform intermediate rounding (i.e.
between arithmetic operations).
It is normal practice to perform the entire calculation
and then report a reasonable number of significant
figures.

The number of significant digits in the result cannot exceed
that in the value with the fewest significant digits.

The result cannot be more precise than any of the values
107 - Introduction to Engineering
32
included in ENGR
the calculation.