Rounding Off Data:

Process of reducing the number of  significant figures in a number from the right side up to the required digits is called rounding off data.

Rules
1= If the digit to be reduce is greater than 5, then reduce it and add 1 to the remaining digit.

Example
2.26 = 2.3 and 4.676 = 4.68 = 4.7
2= if the digit to be reduce is less than 5, then reduce it simply.

Example
2.34 = 2.3 and 4.242 = 4.2
3= If the digit to be reduce is exact 5, then there are two sub rules.
(1) If the digit before 5 is odd (1,3,5,7)
then reduce 5 and ads 1 to it.

Example
2.35 = 2.4 and 4.55 = 4.6
(2) If the digit before 5 is even (2,4,6,8)
then reduce 5 simply

Example
3.45 = 3.4 and 2.65 = 2.6

Rounding Off number without decimal point:

In rounding off the numbers without decimal point give zero on the place of digit to be reduced to maintain the magnitude of the number.

Example
27563 = 27560 = 27600 = 28000

Significant in Addition and Subtraction:
In the addition adn subtraction of the significant figures , maximum number of significant digits to the right side of the decimal point in answer should be equal to the minimum number of significant digits to the right side of the decimal point in any of the given numbers.

Significant Figure in Multiplication and Division:
In the multiplication and division of the significant figures maximum number of total significant figures in answer should be equal to the minimum number of the significant figure in any of the given numbers

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Exponential Notation:

Definition
Short hand notation of very small numbers and very large numbers is known as exponential notation.
Explanation
In exponential notation we write the number in the form of power 10.
It is an easy method to solve the problems of very large and very small numbers.

Parts Of Numbers In Exponential Notation:

(1) Coefficient Part
It is the first intergral of the number in the exponential form which may be form 1 to 9.999 (between 1 and 10) it mean in the coefficient only one non zero digit should be at the left side of the decimal point.

(2) Exponential Part
It is the part of power of 10. In this part 10 is base and the number over 10 is called power or exponent, the power of 10 may be any number and it may be positive or negative.

Rules to Change The Numbers In Exponential Form:

(1) If the decimal point taken to the left side, then the power of 10 will be positive
(2) If the decimal point is taken to the right side then the power of 10 will be negative.


Problems Of The Exponential Notation
1= Multiplication
In multiplication coefficient are multiply and power of 10 (exponent) are added.
2= Division
In the division of exponential numbers, coefficients are added and the power of 10 (exponent) are subtracted.

Logarithm
Definition
Power of 10 for a number is called its logarithm.

Explanation
When the power is raised over the base of 10, it must be equal to the number and power is called logarithm of that number.

Parts Of a Number In Log Value:
There are two parts of a number in a log value.

1) Characteristic
It is the intergral part of the whole number in log value of the power of 10 in the given number.

2) Mantissa
It is the decimal fraction part in log value of a number.
If we change a number in exponential form then mantissa is a log value of its coefficient.


Error And Deviation
Definition:
Difference between the measured and observed value and the actual or most probable value is called error and deviation.

Types Of Error:
There are two types of error.

1) Systematic Error Or Determinate Error:
Error due to the wrong use and the lack in handling of insturemen or system is called systematic error.
This error can be recovered again by the correct use of system of by removing the cause of error so it is called determinate error.
Example
A group of student in laboratory perform experiment of acid and base titration and they observed error in reading because they have not washed the apparatus before experiment or not added indicator in the proper way. Now they can observe correct reading by repeating the experiment again by removing all possibilities of error.

2) Random error or Indeterminate error:
Error due to some unknown defect in the insturement of system is called random error.

Example
The group of student take all precautions, they washed the apparatus, add indicator in the proper way, prepared solution of acid and base in required concentrations, but still the observe error in reading due to unknown cause, this error is random error. This error may be posotive or negative. This error can not be recovered so it is called indeterminate error.
The best way to reduce random error is to take mean of average of different readings in and experiment.
These are the two type of errors which can be found in the field of chemistry and these are certain methods to reduce them.