Fundamental PQ
In multiplication & division, the no. of significant digit in
14. Rules for
the final result is equal to the minimum no of significant Quantities
digits in original no. which are multiplied or divided multiplication & division which
When 2 or more quantities are added or subtracted, can be
13. Rules for addition & measured
in final answer, no. of digits after decimal is equal to
no. which has minimum no. of digits after decimal subtraction & in
terms of
# If a digit to be dropped is less than 5, preceding digit should be left unchanged which
# If a digit to be dropped is greater than 5, preceding digit is increased by 1 12. Rules laws of
# If a digit to be dropped is 5, followed by digit other than 0, preceding digit is increased by 1 for physics
# If a digit to be dropped is 5 or 5 followed by 0, preceding digit remains unchanged if it is even Independent
rounding off 1. can be
# If a digit to be dropped is 5 or 5 followed by 0, preceding digit is increased by 1 if it is odd described.
Physical eg. mass, Radian(rad) [For plane] θ=l/r
@ All non- 0 digits are significant
@ All 0s btw non-zero digits are significant Quantity force etc
Supplementary Units
Steradian(Sr) [For solid angle] d⊖=ds/r²
@ All 0s to right of last non-0 digit are not significant 11. Rules
@ All 0s after a non-0 digit which is after decimal is significant Derived PQ Dependent on eg. acceleration(a)=m/s²=L/T²
@ If a no. is less than 1, all 0s after decimal & before non-0 digit are
for finding PQ=no x unit Q=nu
not significant SF
@ When a quantity is expressed in terms of power of 10, the power of 2. Measurement Comparison of a PQ with a homogeneous quantity of same taken as standard
10 are not significant @ Be easily accessible
Properties of standard @ No change with time
eg. 1.63 here 1 & 6 No. of reliable digits unit/ quantity @No change with physical conditions(temp., pressure etc.
10. Significant
are reliable & 3 is & 1 uncertain digit in @Be of suitable size
uncertain digit measurement are SF Figures/ Digits Units & 3. Units
# MKS(SI unit)- Meter, Kg, sec
Measurement Standard
=> If a Physical eq'n is dimensionally correct, it's not necessary that its numerically correct. 9. Limitations Unit System# CGS- cm, gm, sec
measure of PQ
=> Fails to derive relationship involving trigonometric, logarithmic & exponential function s # FPS- Foot, pound, sec
=> Fails when a PQ depends on more than 3 PQ
of Dimensional
Power to which Fundamental Quantities are to be raised to represent a PQ
=> Value of proportionality constant and dimensionless constant could not be found analysis
4. Dimension
① To convert a PQ from one
system of unit to another. Equation-represents the dimension of any PQ
8.Applications in terms of power of fundamental quantities
Put dimensional formula in value and
check whether LHS = RHS
② To check the accuracy of a physical eq'n. of dimensional
analysis
Taking proportionality and ③ To find relation btw different PQ
forming eq'n and obtain it's formula.
Based on the fact that States that any Physical equation must be
7.Principle of Homogeneity
only similar quantities can dimensionally balanced. It means dimension
be added or subtracted. of terms on LHS must be same as on RHS. of Dimension
Have fixed dimensional formula and fixed Dimensional
value. {eg. universal plank's constant} constant
6.Types of
Have fixed value but no dimensional Dimensionless
constant &
formula. {eg. ⊼ = 22/7} Constant
variables
Have fixed dimensional formula but Dimensional
for
no fixed value. {eg. velocity, force etc} Variable
dimension
Neither have dimensional formula nor Dimensionless
fixed value. {eg. relative density} Variable
In multiplication & division, the no. of significant digit in
14. Rules for
the final result is equal to the minimum no of significant Quantities
digits in original no. which are multiplied or divided multiplication & division which
When 2 or more quantities are added or subtracted, can be
13. Rules for addition & measured
in final answer, no. of digits after decimal is equal to
no. which has minimum no. of digits after decimal subtraction & in
terms of
# If a digit to be dropped is less than 5, preceding digit should be left unchanged which
# If a digit to be dropped is greater than 5, preceding digit is increased by 1 12. Rules laws of
# If a digit to be dropped is 5, followed by digit other than 0, preceding digit is increased by 1 for physics
# If a digit to be dropped is 5 or 5 followed by 0, preceding digit remains unchanged if it is even Independent
rounding off 1. can be
# If a digit to be dropped is 5 or 5 followed by 0, preceding digit is increased by 1 if it is odd described.
Physical eg. mass, Radian(rad) [For plane] θ=l/r
@ All non- 0 digits are significant
@ All 0s btw non-zero digits are significant Quantity force etc
Supplementary Units
Steradian(Sr) [For solid angle] d⊖=ds/r²
@ All 0s to right of last non-0 digit are not significant 11. Rules
@ All 0s after a non-0 digit which is after decimal is significant Derived PQ Dependent on eg. acceleration(a)=m/s²=L/T²
@ If a no. is less than 1, all 0s after decimal & before non-0 digit are
for finding PQ=no x unit Q=nu
not significant SF
@ When a quantity is expressed in terms of power of 10, the power of 2. Measurement Comparison of a PQ with a homogeneous quantity of same taken as standard
10 are not significant @ Be easily accessible
Properties of standard @ No change with time
eg. 1.63 here 1 & 6 No. of reliable digits unit/ quantity @No change with physical conditions(temp., pressure etc.
10. Significant
are reliable & 3 is & 1 uncertain digit in @Be of suitable size
uncertain digit measurement are SF Figures/ Digits Units & 3. Units
# MKS(SI unit)- Meter, Kg, sec
Measurement Standard
=> If a Physical eq'n is dimensionally correct, it's not necessary that its numerically correct. 9. Limitations Unit System# CGS- cm, gm, sec
measure of PQ
=> Fails to derive relationship involving trigonometric, logarithmic & exponential function s # FPS- Foot, pound, sec
=> Fails when a PQ depends on more than 3 PQ
of Dimensional
Power to which Fundamental Quantities are to be raised to represent a PQ
=> Value of proportionality constant and dimensionless constant could not be found analysis
4. Dimension
① To convert a PQ from one
system of unit to another. Equation-represents the dimension of any PQ
8.Applications in terms of power of fundamental quantities
Put dimensional formula in value and
check whether LHS = RHS
② To check the accuracy of a physical eq'n. of dimensional
analysis
Taking proportionality and ③ To find relation btw different PQ
forming eq'n and obtain it's formula.
Based on the fact that States that any Physical equation must be
7.Principle of Homogeneity
only similar quantities can dimensionally balanced. It means dimension
be added or subtracted. of terms on LHS must be same as on RHS. of Dimension
Have fixed dimensional formula and fixed Dimensional
value. {eg. universal plank's constant} constant
6.Types of
Have fixed value but no dimensional Dimensionless
constant &
formula. {eg. ⊼ = 22/7} Constant
variables
Have fixed dimensional formula but Dimensional
for
no fixed value. {eg. velocity, force etc} Variable
dimension
Neither have dimensional formula nor Dimensionless
fixed value. {eg. relative density} Variable
