IEMDaily - Video Lecture Notes

Definition

Fastest speed that some animals can attain

Sr. No.	Name of Object	Speed in km/hr	Speed in m/s
1	Falcon	320	88.88
2	Cheetah	112	31.11
3	Blue fish	40 46	11.11-12.77
4	Rabbit	56	15.55
5	Squirrel	19	5.27
6	Domestic mouse	11	3.055
7	Human	40	11.11
8	Giant tortoise	0.27	0.075
9	Snail	0.05	0.013

Definition

Reporting Numbers

In scientific notation all numbers are written in the form:

m \times 10^{n}

where,

n

is the power.

Definition

Significant Digits

Every measurement involves errors. Thus, the result of measurement should be reported in a way that indicates the precision of measurement. Normally, the reported result of measurement is a number that includes all digits in the number that are known reliably plus the first digit that is uncertain. The reliable digits plus the first digit are known as significant digits or significant figures.
Example: If we say that the period of oscillation of a simple pendulum is

1.62

s, the digits 1 and 6 are reliable and certain, while the digit 2 is uncertain. Thus, the measured value has three significant figures.

Definition

Rules for determining number of significant digits

Rules are as follows:

All the non-zero digits are significant
All the zeros between 2 non-zero digits are significant, no matter where the decimal point is.
If the number is less than 1, the zeros on the right side of decimal point but to the left of the first non-zero digit are not significant (i.e leading zeros are never significant).
In a number with a decimal point, trailing zeros, those to the right of the last non-zero digit, are significant.
The trailing zeros in a number without a decimal point, are not significant.
The trailing zeros in a number with a decimal point, are significant.

For example in 1.001 number of significant digits is 4.

Definition

Reporting errors in measured quantities using rules of significant digits and rounding off

Example: Each side of a cube is measured to be

7.203 m

. What are the total surface area and the volume of the cube to appropriate significant figures?
Solution:
Surface area of the cube

= 6 (7.203)^{2} m^{2} = 311.299254 m^{2} = 311.3 m^{2}

Volume of the cube

= (7.203)^{3} m^{3} = 373.714754 m^{3} = 373.7 m^{3}

Definition

Order of Magnitude and examples

An order of magnitude is an exponential change of plus-or-minus 1 in the value of a quantity or unit. The term is generally used in conjunction with power-of-10 scientific notation.For example, the order of magnitude of

1500

3

, hence

1500

may be written as

1.5 \times 10^{3}

Definition

Rules of Rounding off

The rule by convention is that the preceding digit is raised by

1

if the insignificant digit to be dropped is more than

5

, and is left unchanged if the latter is less than

5

. In the case where the insignificant digit is

5

, the convention is that if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by

1

Definition

Rules for arithmetic operations with significant figures

As there are rules for determining the number of significant figures in directly measured quantities, there are rules for determining the number of significant figures in quantities calculated from these measured quantities.
Only measured quantities figure into the determination of the number of significant figures in calculated quantities. Exact mathematical quantities like in the formula for the area of a circle with radius

r

r^{2}

has no effect on the number of significant figures in the final calculated area. Similarly the in the formula for the kinetic energy of a mass

m

with velocity

v

m v^{2}

, has no bearing on the number of significant figures in the final calculated kinetic energy. The constants and are considered to have an infinite number of significant figures.
For quantities created from measured quantities by multiplication and division, the calculated result should have as many significant figures as the measured number with the least number of significant figures.

For example,