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The digits in a measured quantity which are reliable and confidence
in our measurement + the digit which is uncertain
...
66×10-27 kg
•Electron mass- 10-30 kg

2
...
For example, 5
...
604 has four significant figures; and 4
...


•Earth mass : 1025 kg
•Observable Universe 1055 kg

TIME
•SI unit is second (based on caesium clock with an
uncertainity less than 1 part in 10-13
ie,3μs loss every year)
•Timespan of unstable particle: 10

s

•Age of universe: 10 s
17

•Parallax angle=

BASIS
DISTANCE

b
=x

x

•1 =1
...
91×10­4 rad
...
85×10­6 rad
...
If the digit to be dropped is 5 followed by digits other than zero,
then the preceding digit is raised by one
...
351 is
rounded off to 16
...
758 is rounded off to 6
...


•For very small sizes, optical microscope,
tunneling microscope, electron microscope
were used
...
If the digit to be dropped is 5 or 5 followed by zeros, then the
preceding digit, if it is even, is left unchanged
...
250 becomes 3
...
650 becomes 12
...


•1 AU = 1
...
46 × 1015 m
•1parsec= 3
...
If the digit to be dropped is 5 or 5 followed by zeros, then the
preceding digit, if it is odd, is raised by one
...
750 is rounded off to 3
...
150 is rounded off
to 16
...


•Size of proton: 10-15 m
•Radius Of Earth: 107m
•Distance to Boundary Of
Observable Universe
: 1026 m

RULES FOR ROUNDING OF A MEASUREMENT
ADDITION & SUBTRACTION
In addition or subtraction, the final result should be reported
to the same number of decimal Places as that of the original
number with minimum number of decimal places

SI SYSTEM
7 Base units and 2 supplementary units

1

Length

2

Mass
Time

3
4
5
6
7

NO
...
028
x 1
...
84668

(Three significant figures)
(Answer should have three significant figures
after rounding off)

Answer = 66
...
Unit of permittivity of free space

(a)
(b)
(c)
(d)

coloumb/newton-metre
newton-metre2 /coloumb²
coloumb²/newton-metre2
coloumb2/(newton-metre)2

ε0 is

If L=2
...
1cm,then L+B = ?

Instrumental

1) Pressure=stress=Young‛s modulus=ML T
2) Work=Energy=Torque=M L2 T-2
3)
4)
5)
6)
7)

Power P=M L2 T-3
Gravitational constant G=M-1 L3 T-2
Force constant=Spring constant=M T-2
Coefficient of viscosity=M L-1 T-1
Latent heat L=L2 T-2

8
9

ε

0

Least Count:
Smallest quantity an instrument can
measure
mm scale
↓
1mm

vernier scale
↓
0
...
01mm

VERNIER CALIPERS

1VSD = n-1 MSD
n
n-1
Least Count = 1MSD - n MSD = 1MSD
n
Total Reading = Main Scale Reading + coinciding
Vernier Scale division x least count

Time period

L
R

l
g

α

m
k

R
g

α

= RC = LC

In a vernier calipers, one main scale division is x cm
& n division of vernier scale coincide with n-1 divisions
of the main scale
...

n-1
nx
x
x
a) ( n ) x
b)
c)
d) n
(n-1)
(n-1)

SCREW GAUGE

DIMENSIONLESS
QUANTITIES

Main Scale Reading
Pitch =
No
...
of divisions on
circlular scale

Total Reading = Linear Scale Reading + circular scale
reading x least count

In SI Units, the dimensions of ε

0

μ0

(a) 4
...
43 cm

a)A-1 T M L3

b)A T2 M-1L-1

(c) 4
...
of divisions on its circular
scale required to measure 5μm diameter of wire is
a) 200 b) 50

c) 400 d) 100

Δamean
amean

x 100

COMBINATION OF ERRORS

Operations

Absolute
error Δ Z

Formula Z

Relative
error ΔZ/Z

Percentage error
100 x Δ Z / Z

Sum

A+B

ΔA+ ΔB

ΔA+ΔB
A+B

ΔA+ΔB
A+B

x 100

Difference

A-B

ΔA+ ΔB

ΔA+ΔB
A-B

ΔA+ΔB
A-B

x 100

AxB

AΔB+ BΔA

Division

A
B

BΔA+ AΔB

Power

An

Multiplication

A

Root

1/n

B2

ΔA

A

+

ΔA

A

+

ΔB

B
ΔB

B

( A + B ( x 100
( AA+ BB(x 100

n

1 A 1/n-1 ΔA
n

1 ΔA
n A

Δ

Δ

ΔA

n A n - 1 ΔA

ΔB

ΔA

A

n

ΔA x 100

A

1 ΔA x 100
n A

General rule:
If Z = APBq

Cr

Tα

Δamean
amean

• Percentage Error:-

If n VSD Coincides with (n-1)
MSD,
then (n-1) MSD= n VSD

10) Capacitance=M-1 L-2 T-4 A2
11) Permittivity ε0=M-1 L-3 T4 A2
12) Angular momentum = planck‛s constant
=M1 L2 T-1

a1+a2+a3+
...
+Δan
n

• Absolute Error :- Δa = |ai-amean|, amean=

Least Count = 1 MSD - 1VSD

I
=M L2 T-3 A-2

μ0

-2

Personal

Due to individual
bias,Lack of proper
setting of apparatus

Limitations in
experimental
technique

• Least count error is the smallest value that can be measured by
instrument (occurs with random & systematic errors)

INSTRUMENTS
-1

Irregular and at random
in magnitude & direction

Experimental

Due to inbuilt defect
of measuring instrument

• Relative Error:-

Answer = 3
...
1421
0
...
09
3
...
Trailing zeros or the zeros placed to the right of the number are
significant
...
330 has four significant figures; 433
...
000 has six significant figures
...
If the digit to be dropped is more than 5, then the preceding digit
is raised by one
...
87 is rounded off to 6
...
78 is rounded off to 12
...


-2

NO
...
Leading zeros or the zeros placed to the left of the number are
never significant
...
543 has three significant figures;
0
...
006 has one significant
figure
...
If the digit to be dropped is less than 5, then the preceding digit is
left unchanged
...
82 is rounded off to 7
...
94 is rounded off to 3
...


Systematic Errors

APPLICATIONS

RULES FOR ROUNDING OF A MEASUREMENT

p

•Large distance is measured by
parallax method

Difference between true value
& measured value of a quantity

Dimensions of a physical quantity are power to which units of base quantity
are raised
...
In exponential notation, the numerical portion gives the number of
significant figures
...
32 x 10-² has three significant
figures and 1
...


MEASUREMENT OF LENGTH

ERRORS IN MEASUREMENT

Dimensional Analysis

RULES FOR SIGNIFICANT FIGURES
1
...
For example, 42
...
4 has four significant figures; and 24
...


-24

UNITS & MEASUREMENTS

SIGNIFICANT FIGURES

MEASUREMENT OF MASS & TIME

,Then the maximum fractional relative
error in Z will be:
ΔZ =p ΔA +q ΔB

Z

A

B

+r ΔC

C

In an expirement four quantities a,b,c
and d are measured with percentage
error1%, 2%, 3% and 4% respectievely

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