PHYSICS for CLASS XI ! Simplified

NCERT Chapter – 2: Units and Measurement (Except Dimension)

Precision and Accuracy : The accuracy of a measurement is a measure of how close the measured value is to the true value of the quantity. Precision tells us to what resolution or limit the quantity is measured.

Example. If the true value of measurement is 6.786, Instrument A reads as 6.8 and instrument B reads as 6.645, then instrument A is more accurate but instrument B is more precise.   

Order of Magnitude :

The order of magnitude of a quantity gives us a value nearest to the actual value of the quantity, in terms of suitable power of 10 . It gives an idea about how big or how small a given physical quantity is

• To determine the order of magnitude (x) of a number N, we express it as  N = n x 10^x                                                                                            If  0.5 ≤ n <5, then x will be the order of magnitude of N.

Example :

1.Measured number is 49 .Expressed in nearest power of 10 : 4.9 x 10¹

Order = 1

2. Measured number is 753000 .Expressed in nearest power of 10 : 0.753 x10 ⁶.

Order = 6.

3. Measured number is .135.Expressed in nearest power of 10 : 1.35 x 10 ^-1 .

Order = -1.

Significant Figures

• All the non – zero digits are significant . so 14.82 has four significant figures.
• All the zeros between two non – zero digits are significant , no matter where the decimal point is , if at all . Thus 100 . 05 km has five significant figures .
• If the number is less than 1 , the zero(s) on the right of decimal point but to the left of the first non – zero digit are not significant .
• The terminal or trailing zero(s) in a number without a decimal point are not significant .For example , 86400 has three significant figures .
• The trailing zero(s) in a number with a decimal point are significant . For example : 3.500 have four significant figures each .
• The number of significant figures does not depend on the system of units . So 16.4 cm , 0.164 m and .000164 km , all have three significant figures .

<script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>
<ins class="adsbygoogle"
     style="display:block; text-align:center;"
     data-ad-layout="in-article"
     data-ad-format="fluid"
     data-ad-client="ca-pub-1841555201014310"
     data-ad-slot="6301174304"></ins>
<script>
     (adsbygoogle = window.adsbygoogle || []).push({});
</script>

Significant Notation

A number is expressed in the power of 10 as a x 10^b, where a is the number between 1 and 10, and b is any positive or negative exponent of 10 . The decimal point is written after the first digit .

For example : Length of rod is reported as 3.500 m . In scientific notation , it can be expressed as different units as

3.500 m = 3.500 x 10² cm = 3.500 x 10³ mm = 3.500 x 10^-3 km .

We retain only those zeros in the base number which are the result of a measurement . Now the power of 10 is not relevant to the determination of significant figures . Each of the above numbers has four significant figures .

Rules for Arithmetic Operations with Significant Figures

• Significant figures in the sum or difference of two numbers.                  In addition or subtraction , the final result should retain as many decimal places as are there in the number with the least decimal places
• Significant figures in the product or quotient of two numbers. The final result should be reported to the number of significant figures as that of the original number with minimum number of significant figures.

Rounding off the Uncertain Digits

• Rule -1 : If the digit to be dropped is less than 5 , then the preceding digit is left unchanged .                                                 Eg : x = 6.83 is rounded off to 6.8
• Rule – 2 : If the digit to be dropped is more than 5 , then the preceding digit is raised by one.                                           Eg : x = 8.87 is rounded off to 8.9
• Rule – 3 : If the digit to be dropped is 5 followed by digits other than zero , then the preceding digit is raised by one .     Eg : 17.351 is rounded off to 17.4
• Rule – 4 : If the digit to be dropped is 5 or 5 followed by zeros , then the preceding digit is left unchanged , if it is even    Eg: x= 4.450 becomes 4.4 on rounding off .
• Rule – 5 : If the digit to be dropped is 5 or 5 followed by zeros , then the preceding digits is raised by one , if it is odd .    Eg : x = 3.750 is rounded off to 3.8.

https://youtu.be/Lxbovafwmzc

ERROR ANALYSIS

No value in Physics perfect, every value not certain approximations. In other words every measurement is approximate due to some measurement. In measurement, we further classify errors as systematic error and  random errors.

Systematic Errors

systematic errors are those errors that tend to be in one direction, is positive or negative

(1) First is instrumental error that arise with error due to design of instrument,

(2) Second is due to imperfection in technique, in this error flaw in the procedure is taken

(3) Third is personal error that is due to lack of proper setting of apparatus by individuals carelessness

Random Errors 

Random errors are errors which occur regularly.

Least Count Error

The smallest value that can be measured by the measuring instrument is called its least count.

All the readings or measured values are good only up to this value only.

Download Notes Here