In addition or subtraction , the result should be reported to the same number of decimal places as that of the number with minimum number of decimal places. In multiplication or division, the result should be reported to the same number of significant figures as that of the number with minimum of significant figures.
Accuracy refers to the closeness of a measurement to the true value of the physical quantity and precision refers to the resolution or the limit to which the quantity is measured. The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. While rounding off measurements the following rules are applied Rule I: If the digit to be dropped is smaller than 5,then the preceding digit should be left unchanged. For ex: 9. For ex: 5.
M 1 L 1 T -2 is the dimensional formula of Force. Dimensional Costants: These are the quantities which possess dimensions and have a fixed value.
Ex: Gravitational Constant. Dimensional Variables: These are the quantities which possess dimensions and do not have a fixed value For ex: velocity, acceleration etc. Dimensionless Constants: these are the quantities which do not possess dimensions and have a fixed value. Dimensionless Variables: These are the quantities which are dimensionless and do not have a fixed value.
For ex: Strain, Specific Gravity etc. A given physical relation is dimensionally correct if the dimensions of the variousterms on either side of the relation are the same.
They have to be determined either by experiment or by mathematical investigation. It fails in case of exponential and trigonometric relations. Copyright ncerthelp. Units of Measurement Physics Class 11 Download in pdf Measurement of physical quantities Physics is a quantitative science, based on measurement of physical quantities. Base quantity and Fundamental Units Each base quantity is defined in terms of a certain basic arbitrarily chosenbut properly standardised reference standard called unit such as metre,kilogram,second,ampere,kelvin,mole,and candela.
Fundamental Quantities Fundamental Units Symbol 1. Length metre m 2. Mass kilogram kg 3. Time second S 4. Temperature kelvin kg 5 Electric current ampere A 6 Luminous intensity candela cd 7 Amount of substance mole mol. Follow Us On Facebook. Please Share this webpage on facebook, whatsapp, linkdin and twitter.
Relative Error can be defined as the mean absolute error divided by the mean value of the quantity measured. Percentage Error can be defined as the relative error expressed in percentage. When a quantity is dependent on two or more other quantities, the combination of errors in the two quantities will be helping for determining and predicting the errors in the resultant quantity. There are various procedures for this. Sum or Difference. Raised to Power. Resultant value Z.
Result with error. Sum of absolute errors. Sum of relative errors. Every measurement gives us an output in a number that is included of reliable digits and uncertain digits.
Reliable digits added with the first uncertain digit can be defined as significant digits or significant figures. This is representing the precision of measurement which is dependent on least count of instrument used for measurement. The period of oscillation of a pendulum is 1. Here 1 and 6 will be the reliable and 2 is uncertain. Hence, the measured value will be having three significant figures. All non-zero digits will be significant. Irrespective of decimal place, all zeros between two non-zero digits will be significant irrespective of decimal place.
Zeroes before non-zero digits and after decimal are not considered as significant, for a value less than 1.
Zero present before decimal place in case of these number will be insignificant always. Trailing zeroes in case of a number without any decimal place will be insignificant. Trailing zeroes in case of a number with decimal place will be significant. Variation of units will not change number of significant digits. As an example,. Here, first two quantities are having 4 but third quantity is having 2 significant figures.
Make use of scientific notation for reporting measurements. Here, as the power of 10 is being irrelevant, number of significant figures will be 4. Multiplying or dividing exact numbers will be giving infinite number of significant digits. In this case, 2 can be represented as 2, 2. Multiplication or. Addition or Subtraction.
The end result must retain as many significant figures as there in the initial number with the least number of significant digits. The end result must have as many decimal places similar way as in the original number with the least decimal places.
Addition of As Rounding off will be essential for reducing the number of insignificant figures to hold to the rules of arithmetic operation with significant figures.
Rule Number. Insignificant digit. Preceding digit. Example rounding off to two decimal places. Insignificant digit to be dropped. Preceding digit is.
Number— 3. Result —3. Preceding digit is left unchanged. Insignificant digit to be dropped being equal to 5. When preceding digit is even, it is left unchanged. When preceding digit is odd, it is raised by 1. For calculating the uncertainty, below process must be used. Do summation of a lowest amount of uncertainty in the original numbers. Example uncertainty for 3. Find out these in percentage also. In the uncertainty, round off the decimal place for obtaining the end uncertainty result.
For example, for a rectangle,. When we multiply,. The relative error of a value of number mentioned to significant figures will be dependent on n and on the number itself. As an example, say accuracy for two numbers 1. But relative errors are:. Therefore, the relative error will be dependent upon number itself.
The results in the intermediate step of a multi-step computation should be found to have one significant figure more in all the measurement than the number of digits in the least precise measurement. Therefore, taking one extra digit will be providing more precise outputs and reduces rounding off errors. The powers exponents to which base quantities are raised to represent that quantity can be defined as dimensions of a physical quantity.
They are figured as the square brackets around the quantity. Dimensions of the 7 base quantities has been considered as — Length [L], time [T], Mass [M], thermodynamic temperature [K], luminous intensity [cd], electric current [A] and amount of substance [mol]. For example,. The other dimensions for a quantity will be always 0. As an example, in the case of volume only length has 3 dimensions but the mass, time. Dimensions will not affect the magnitude of a quantity Dimensional formula and Dimensional Equation.
The expression which is representing how and which of the base quantities represent the dimensions of a physical quantity is defined as Dimensional Formula. An equation we got after equating a physical quantity with its dimensional formula is a Dimensional Equation. Physical Quantity. Dimensional Formula. Dimensional Equation. Mass Density. The physical quantities which is having similar dimensions only can be added and subtracted.
This can be named as the principle of homogeneity of dimensions. Dimensions are multipliable and can be cancelled as normal algebraic methods. Quantities on both sides should always have identical dimensions, in mathematical equations.
Arguments of special functions such as trigonometric, logarithmic and ratio of similar physical quantities will be dimensionless. Equations will be uncertain to the extent of dimensionless quantities. In Dimension terms,. When we check the Dimensional Consistency of equations.
A dimensionally correct equation should be having identical dimensions on both sides of the equation. There is no need for a dimensionally correct equation to be a correct equation but a dimensionally incorrect equation will be always incorrect.
Dimensional validity can be tested but not calculate the correct relationship between the physical quantities. Dimensions on both sides will be [L] because [T] get cancelled out. Therefore this will be dimensionally correct equation. For deducing a relation among physical quantities, we must know the dependence of one quantity over others or independent variables and assume it as a product type of dependence. Dimensionless constants will not be obtainable by the use of this method.
We can take an example,. Here 5. The units that can be expressed independently are called fundamental or base units. For example- mass is expressed in kilogram, length in metre, and time in second respectively are fundamental units. The units for which a combination of the fundamental units is called derived units. The base units for length, mass and time in unit systems are:. CGS System: centimetre, gram and second. FPS System: foot, pound and second. MKS System: metre, kilogram and second.
Length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity are expressed in metre m , kilogram kg , second s , ampere A , Kelvin K , mole mol and candela cd respectively. Apart from the above units, there are two supplementary base units:. Image to be added soon. This method is used to measure large distances like that of planets and stars from earth. In Chapter 2 Physics Class 11 Notes, one can learn how to measure the size of a molecule.
Some units of short length:. The uncertainty while measuring a physical quantity is called an error. Instrumental errors. A flaw in experimental technique or procedure. Personal errors. Least Count Error: associated with the resolution of the instrument.
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