Significant Figures in Electronic Instrumentation
Topic –
Introduction to Electronic Instrumentation and
Measurements
Presented by
Dr. S. D. More
Assistant Professor & Head
Department of
Physics
Deogiri College, Aurangabad
Paper – II: Instrumentation - II
B. Sc. First Year (Instrumentation Science)
1. Introduction to Electronic
Instrumentation and
Measurements
•
Much of our everyday experience deals with exact
numbers of things i. e.
6 stamps, 7.50 dollars and 7
people.
•
These items can be counted and an exact numerical
representation provide' all figures are significant in
such cases. But in other situations, you may take
measurement; that are subject to errors.
•
For example
, 1) you might measure the height of a
person as 67, 68, or 69 in, depending on how straight
the person stands.
•
2) How many people do you know who own a
perfectly accurate watch that never needs to be
reset"!
None!
•
These flaws are implicitly resolved when we apply
the concept of
significant figures
to the
measurements.
•
This concept demands that we
impute no more
precision or accuracy to a measurement or
calculation than the natural physical reality of the
situation permits.
•
The counting numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) are
always significant.
•
Zero is significant
only if it is used to indicate exactly
zero, or a truly null case.
•
Zero is
not significant
if it is used merely as a place
holder to make the numbers look nicer on the
printed page.
–
For example, if "0.60" is properly written, then it means
exactly
6/10 not "approximately 0.6“.
•
The zero used here in the hundredth place is
significant.
•
If the number is written "0.6," then we may assume
that it means 6/10 plus or minus some amount of
either error or uncertainty.
•
When we use numbers to indicate a quantity, the
concept of significant figures becomes important.
•
For example, "16 gal" has two significant figures but
can reasonably be taken to mean that the quantity of
liquid is somewhere between 15 and 17 gal.
•
But if our liquid measuring device is better, then we
might write "16.0 gal" to indicate precisely 16 gal
pIus or minus a very small error.
•
Perhaps the real value is between 15.9 and 16.1 gal.
•
Consider a pressure gauge that is guaranteed to an
accuracy of ±5%. A reading of "100 torr" has three
figures, meaning that the actual pressure is between
[100
-
5%] and [100
+
5%], or 95 to 105 torr (two
significant figures).
•
Consider a practical measurement situation. An
experiment uses a digital voltmeter to measure an
electrical potential difference of exactly 15 V.
•
The instrument reads from 00.00 to 19.99 V, with an
accuracy of ±1%.
•
In addition, digital voltmeters typically have a ±1-digit
error in the least significant position due to their design;.
•
This problem is called
last digit bobble.
•
For the digital voltmeter in question,
19.99
•
Most significant digit
Least significant digit
•
The "last digit bobble" problem means that a reading of
15.00 V could represent any value between 15.00 - 00.01
(i.e. 14.99) V and 15.00 + 00.01 (i.re. 15.01) V.
•
In addition, the error of 1% means that the actual voltage
could be ± (15 x 0.01) = 0.15 V.
•
Thus, the actual voltage could be from (15.00 - 0.15) V to
(15.00 + 0.15) V, or a range of +14.84 to +15.16 V.
•
If both errors are minus,
Reading:
15.00 V
—0.01 V
—0.15 V
14.84 V (worst case)
•
or, if both errors are positive,
Reading:
15.00 V
+0.15 V
+0.01 V
5.16 V (worst case)
•
Significant figure errors are propagated in
calculations.
•
A rule to remember is that
the number of significant
figures is not improved by combining the numbers
with other numbers
.
•
For example, multiplying a significant digit by a non-
significant digit yields a result that has at least one
non-significant digit. Often the number of significant
figures decreases in calculation.
•
Significant figure rules were perhaps a little easier to
understand and use in the days when scientists and
engineers calculated on slide rules.
•
Those tools were limited to two or three digits, so
one was less tempted to write down a very long
number.
•
But in this age of
10-digit scientific pocket
calculators
, and the nearly universal distribution of
personal computers
, the distinction often gets lost.
•
Consider a simple electrical problem as an example.
One expression of Ohm's law states that the current
I
flowing in a circuit is the quotient of the voltage V
and the resistance
R.
•
Suppose that 10 V is applied to a 3
resistance.
•
According to pocket scientific calculator, the current
is
10 V/3
= 3.333333333 A.
•
Does anyone really think that their ordinary,
laboratory ammeter can measure to within 10
-9
A
(i.e., 3.33 nA)?
•
In most cases we would be exaggerating to claim
more than 3.33 or 3.333 A (at most) with very high
quality meters with recent calibration stickers on
them!
•
Indeed, on most lower-quality instruments, "3" or
"3.3"would be a more reasonable statement of the
current reading.
•
Being mindful of significant figures is a key factor in
making good electronic measurements and
maintaining the integrity and credibility of the
measurement system.
Scientific Notation
•
Scientific notation
is a simple arithmetic shorthand
that allows one to
deal with very large or very small
numbers using only a few digits between 1 and 10
and using powers-of-10 exponents.
•
The form of a number in scientific notation is
•
For example
, if the age of a college physics
professor is 47 years, it could be written
Prof's age = 4.7 x 10
1
years
Standard values in powers of 10 notation
along with respective Prefix
Metric Prefix
Physical Units
Physical Constants
Everyday measurements often require significant figures to account for precision and accuracy. Learn about the importance of significant figures in electronic instrumentation, how to interpret them, and why they are crucial for precise measurements in scientific fields such as physics.
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Presentation Transcript
Topic Introduction to Electronic Instrumentation and Measurements Presented by Dr. S. D. More Assistant Professor & Head Department of Physics Deogiri College, Aurangabad
B. Sc. First Year (Instrumentation Science) Paper II: Instrumentation - II
1. Introduction to Electronic Instrumentation and Measurements
Much of our everyday experience deals with exact numbers of things i. e. 6 stamps, 7.50 dollars and 7 people. These items can be counted and an exact numerical representation provide' all figures are significant in such cases. But in other situations, you may take measurement; that are subject to errors. For example, 1) you might measure the height of a person as 67, 68, or 69 in, depending on how straight the person stands.
2) How many people do you know who own a perfectly accurate watch that never needs to be reset"! None! These flaws are implicitly resolved when we apply the concept of significant measurements. figures to the This concept demands that we impute no more precision or accuracy calculation than the natural physical reality of the situation permits. to a measurement or The counting numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) are always significant.
Zero is significant only if it is used to indicate exactly zero, or a truly null case. Zero is not significant if it is used merely as a place holder to make the numbers look nicer on the printed page. For example, if "0.60" is properly written, then it means exactly 6/10 not "approximately 0.6 . The zero used here in the hundredth place is significant. If the number is written "0.6," then we may assume that it means 6/10 plus or minus some amount of either error or uncertainty.
When we use numbers to indicate a quantity, the concept of significant figures becomes important. For example, "16 gal" has two significant figures but can reasonably be taken to mean that the quantity of liquid is somewhere between 15 and 17 gal. But if our liquid measuring device is better, then we might write "16.0 gal" to indicate precisely 16 gal pIus or minus a very small error. Perhaps the real value is between 15.9 and 16.1 gal.
Consider a pressure gauge that is guaranteed to an accuracy of 5%. A reading of "100 torr" has three figures, meaning that the actual pressure is between [100 - 5%] and [100 + 5%], or 95 to 105 torr (two significant figures). Consider experiment uses a digital voltmeter to measure an electrical potential difference of exactly 15 V. The instrument reads from 00.00 to 19.99 V, with an accuracy of 1%. In addition, digital voltmeters typically have a 1-digit error in the least significant position due to their design;. This problem is called last digit bobble. a practical measurement situation. An
For the digital voltmeter in question, 19.99 Most significant digit Least significant digit The "last digit bobble" problem means that a reading of 15.00 V could represent any value between 15.00 - 00.01 (i.e. 14.99) V and 15.00 + 00.01 (i.re. 15.01) V. In addition, the error of 1% means that the actual voltage could be (15 x 0.01) = 0.15 V. Thus, the actual voltage could be from (15.00 - 0.15) V to (15.00 + 0.15) V, or a range of +14.84 to +15.16 V.
If both errors are minus, Reading: 15.00 V 0.01 V 0.15 V 14.84 V (worst case) or, if both errors are positive, Reading: 15.00 V +0.15 V +0.01 V 5.16 V (worst case)
Significant calculations. figure errors are propagated in A rule to remember is that the number of significant figures is not improved by combining the numbers with other numbers. For example, multiplying a significant digit by a non- significant digit yields a result that has at least one non-significant digit. Often the number of significant figures decreases in calculation. Significant figure rules were perhaps a little easier to understand and use in the days when scientists and engineers calculated on slide rules.
Those tools were limited to two or three digits, so one was less tempted to write down a very long number. But in this age of 10-digit scientific pocket calculators, and the nearly universal distribution of personal computers, the distinction often gets lost. Consider a simple electrical problem as an example. One expression of Ohm's law states that the current I flowing in a circuit is the quotient of the voltage V and the resistance R. Suppose that 10 V is applied to a 3 resistance.
According to pocket scientific calculator, the current is 10 V/3 = 3.333333333 A. Does anyone really think that their ordinary, laboratory ammeter can measure to within 10-9A (i.e., 3.33 nA)? In most cases we would be exaggerating to claim more than 3.33 or 3.333 A (at most) with very high quality meters with recent calibration stickers on them! Indeed, on most lower-quality instruments, "3" or "3.3"would be a more reasonable statement of the current reading.
Being mindful of significant figures is a key factor in making good electronic maintaining the integrity and credibility of the measurement system. measurements and
Scientific Notation Scientific notation is a simple arithmetic shorthand that allows one to deal with very large or very small numbers using only a few digits between 1 and 10 and using powers-of-10 exponents. The form of a number in scientific notation is
For example, if the age of a college physics professor is 47 years, it could be written Prof's age = 4.7 x 101years
Standard values in powers of 10 notation along with respective Prefix
