Tips and shortcuts on Integers, Fractions, Prime and Composite

Objectives

• Classification of real numbers
• Terminating and Recurring decimals
• Conversion from recurring decimal to fraction
• Comparison of fractions
• Integers (odd and even) and its properties
• Prime and composite numbers
• Summation results

Classification of Real Numbers

It is possible to design a family tree of numbers in the following manner. 

Rational Numbers

Any number which can be expressed in the form p/q, where p and q are integers (both + and -) and q≠0
, is called a rational number. Eg: 12,−34,5,0,−7 etc.

Irrational Numbers

Obviously this is the number which can't be expressed in the form pq
, where p and q are integers (both + and -) and q≠0. Eg: 2√,π,e etc. For a clear understanding about irrational numbers, it is better to consider the classification of Decimal Numbers.

Terminating and Non-terminating Decimals

If the decimal part of a number consisting a finite number of digits, then it is terminating decimal, otherwise it is a non-terminating decimal.
Eg: 0.2,1.25,123.12345
etc are the examples for terminating decimals.
0.333...,0.1542782157... are the examples for non-terminating decimal.

Recurring Decimal

In a non-terminating decimal if the decimal part is an infinite repetition of a number or a group of numbers, and then it is called a recurring decimal.
Eg: 0.33333... (only 3 repeating), this can be expressed as 0.3¯

0.545454... (pair 54 repeating), this can be expressed as 0.54¯¯¯¯
0.12366666... (only 6 repeating), this can be expressed as 0.1236¯

Definition for irrational numbers

If a decimal is non-terminating and non-recurring, then it is an irrational number. Eg: 2√=1.414213562...,3√=1.7320508...