Number

Natural Numbers:

The natural numbers include whole numbers except 0.

E.g. 1,2,3,4,5,6…

Integers:

Positive natural numbers, negative natural numbers along with 0 are called integers.

-1,-2,-3,0,+1,+2,+3…

Prime Numbers:

A prime number is a number with exactly two factors (i.e. 1 and itself (1×3))

E.g. 2,3,5,7,111,13,17,19,23,29,31…

Composite Numbers:

Those numbers which have more than two factors.

E.g. 4,6,8,9,10,12,14,15,16,18,20…

Factors:

The factors of a number are the natural numbers which divide exactly into that number (without a remainder).

8:  1×8             12:  1×12

2×4                     2×6

3×4

Multiples:

Multiples of a number are numbers in its times table.

Multiples of 5 are 5, 10, 15, 20, 25, 30…

 

Highest Common Factor (HCF):

It is the highest factor which is common to all of the given numbers.

E.g.  8:  1×8                 12:  1×12

2×4                          2×6               In this example the common factors are 1, 2, 4 and the

3×4                Highest factor is 4; therefore the HCF of 12 and 8 is 4. 

In this example the common factors are 1, 2, 4 and the highest factor is 4; therefore the HCF of 12 and 8 is 4. 

 

Rational Number:

A rational number is one which can be expressed in the form   where a and b are integers and b is not equals to 0.

Irrational Number:

Numbers that can’t be expressed as as a fraction or a ratio of 2 integers are known as irrational numbers.

Real Numbers:

These include all rational, irrational, fractions and integers.

Terminating Decimals:

These are decimal numbers which stop after a certain number of decimal places.

E.g. 7/8 = 0.875 it stops after three decimal places.

Recurring Decimals:

These are decimal numbers which keep repeating a digit or a group of digits.

E.g. 137/259 = 0.528 957 528 957 528 957… the six digits 528 957 repeat in this order.

Even Number:

Numbers which are divisible by 2

E.g. 2, 4, 6, 8…

Odd Number:

Numbers which are not divisible by 2

E.g. 1, 3, 5, 7

Square Number:

It is the result of multiplying  a number by itself.

E.g. 1², 2², 3² ….. 1, 4, 9….

Cube Number:

It is the result of multiplying a number by itself 3 times.

E.g. 1³, 2³, 3³ …. 1, 8, 27….

Significant Figures:

The following are few examples showing clearly what is meant by significant figures.

8064 = 8000 (correct to 1 significant figures)

8064 = 8100 (correct to 2 significant figures)

8064 = 8060 (correct to 3 significant figures)

0.00208 = 0.005 (correct to 1 significant figures)

0.00208 = 0.0021 (correct to 2 significant figures)

3.00508 = 3.01 (correct to 3 significant figures)

Decimal Places:

The following are few examples showing clearly what is meant by decimal places.

0.0647 = 0.1 (correct to 1 dp)

0.0647 = 0.06 (correct to 2dp)

0.0647 = 0.065 (correct to 3dp)

2.0647 = 2.065 (correct to 3dp)

Test Of Divisibility: