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NUMBER SYSTEM CONCEPTS - BASIC AND INTERACTIVE
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Number System Complete Notes
NUMBER SYSTEM CONCEPTS - BASIC AND INTERACTIVE
1. Natural Numbers
Natural numbers are counting numbers starting from 1.
Natural Numbers = 1, 2, 3, 4, 5, ...
Example:
1, 7, 25 and 100 are natural numbers.
2. Whole Numbers
Whole numbers include 0 along with all natural numbers.
Whole Numbers = 0, 1, 2, 3, 4, ...
Example:
0, 5 and 89 are whole numbers.
3. Integers
Integers include positive numbers, negative numbers and zero.
..., -3, -2, -1, 0, 1, 2, 3 ...
Example:
-7, 0 and 15 are integers.
4. Even Numbers
Numbers divisible by 2 are called even numbers.
Example:
2, 4, 6, 8 and 10 are even numbers.
Even Number ÷ 2 = No remainder
5. Odd Numbers
Numbers not divisible by 2 are called odd numbers.
Example:
1, 3, 5, 7 and 9 are odd numbers.
6. Prime Numbers
A prime number has only two factors: 1 and itself.
Example:
2, 3, 5, 7 and 11 are prime numbers.
Prime Number
Factors
5
1, 5
7
1, 7
7. Composite Numbers
Composite numbers have more than two factors.
Example:
4, 6, 8 and 12 are composite numbers.
8. Factors and Multiples
Factors divide a number exactly. Multiples are obtained by multiplying numbers.
Example:
Factors of 12 = 1,2,3,4,6,12
Multiples of 5 = 5,10,15,20...
9. HCF and LCM
HCF means Highest Common Factor.
LCM means Least Common Multiple.
Example:
Factors of 12 = 1,2,3,4,6,12
Factors of 18 = 1,2,3,6,9,18
HCF = 6
Multiples of 4 = 4,8,12,16,20...
Multiples of 6 = 6,12,18,24...
LCM = 12
10. Place Value
The value of a digit according to its place is called place value.
Example:
In 456:
4 → 400
5 → 50
6 → 6
11. Face Value
The face value of a digit is the digit itself.
Example:
In 782:
Face value of 8 = 8
12. Ascending and Descending Order
Ascending order means smallest to greatest.
Descending order means greatest to smallest.
Ascending:
2, 4, 8, 10
Descending:
10, 8, 4, 2
13. Roman Numerals
Roman numerals are ancient number symbols.
Roman
Number
I
1
V
5
X
10
L
50
C
100
14. Indian Number System
Indian system uses lakhs and crores.
Example:
45,67,890
Read as:
Forty five lakh sixty seven thousand eight hundred ninety.
15. International Number System
International system uses millions and billions.
Example:
4,567,890
Read as:
Four million five hundred sixty seven thousand eight hundred ninety.
16. Binary Number System
Binary system uses only two digits: 0 and 1.
Example:
1010 is a binary number.
17. Decimal Number System
Decimal system uses digits from 0 to 9.
Example:
256, 789 and 1000 are decimal numbers.
18. Square Numbers
A square number is obtained by multiplying a number by itself.
5 × 5 = 25
Example:
1, 4, 9, 16 and 25 are square numbers.
19. Cube Numbers
Cube numbers are obtained by multiplying a number three times.
3 × 3 × 3 = 27
Example:
8, 27 and 64 are cube numbers.
20. Scientific Notation
Scientific notation expresses very large or small numbers.
4500000 = 4.5 × 10⁶
Example:
Used in science and astronomy.
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Interactive Number System Learning
Interactive Learning of Number System
1. Introduction to Numbers
Numbers help us count, measure and compare things.
Example:
5 apples, 10 students and 100 books.
Numbers are used everywhere in daily life.
2. Digits and Numerals
Digits are symbols used to make numbers.
0,1,2,3,4,5,6,7,8,9 are digits.
A numeral is formed using digits.
Example:
5 is a digit.
356 is a numeral.
Enter a numeral:
Check Digits
3. Number Line
A number line shows numbers in order.
0
1
2
3
4
5
Numbers increase from left to right.
4. Counting Numbers
Counting numbers are numbers used for counting objects.
1, 2, 3, 4, 5...
Example:
1 pen, 2 books, 3 chairs.
5. Natural Numbers
Natural numbers begin from 1.
1,2,3,4,5...
Example:
7, 25 and 100 are natural numbers.
Enter a number:
Check
6. Whole Numbers
Whole numbers include zero.
0,1,2,3,4,5...
0 is the smallest whole number.
7. Integers
Integers include positive numbers, negative numbers and zero.
..., -3,-2,-1,0,1,2,3...
-5, 0 and 8 are integers.
8. Positive Integers
Positive integers are numbers greater than zero.
1,2,3,4...
7 and 25 are positive integers.
9. Negative Integers
Negative integers are numbers less than zero.
-1,-2,-3,-4...
-7 and -20 are negative integers.
10. Rational Numbers
Rational numbers can be written in the form p/q.
p/q where q ≠ 0
1/2, 3/4 and 5 are rational numbers.
11. Irrational Numbers
Irrational numbers cannot be written in the form p/q.
√2 and π are irrational numbers.
12. Real Numbers
Real numbers include rational and irrational numbers.
5, -3, 1/2 and √2 are real numbers.
13. Imaginary Numbers
Imaginary numbers involve √-1.
i = √-1
3i and 5i are imaginary numbers.
14. Complex Numbers
Complex numbers contain real and imaginary parts.
a + bi
3 + 2i and 5 - i are complex numbers.
Enter a complex number:
Check
Interactive Number System Quiz
Interactive Number System Quiz
1. Which is the smallest natural number?
0
1
-1
10
Correct Answer: 1
Natural numbers begin from 1.
2. Which is the smallest whole number?
0
1
2
-1
Correct Answer: 0
Whole numbers start from 0.
3. Which of the following is NOT a whole number?
5
0
99
-3
Correct Answer: -3
Whole numbers do not include negative numbers.
4. Which number lies exactly between 8 and 10?
7
11
9
12
Correct Answer: 9
9 comes between 8 and 10.
5. Which is a negative integer?
-12
12
0
3
Correct Answer: -12
Negative integers are less than zero.
6. Which number is irrational?
1/2
√2
5
0
Correct Answer: √2
√2 cannot be written as p/q.
7. Which is a rational number?
π
√5
3/4
√7
Correct Answer: 3/4
3/4 can be written as p/q.
8. Which is an imaginary number?
5
0
7/2
3i
Correct Answer: 3i
Imaginary numbers contain i.
9. Which is a complex number?
5
3 + 2i
√2
0
Correct Answer: 3 + 2i
Complex numbers have real and imaginary parts.
10. How many digits are there in the decimal number system?
10
5
2
100
Correct Answer: 10
Digits are 0 to 9.
11. Which is NOT an integer?
-5
0
8
1/2
Correct Answer: 1/2
Integers do not contain fractions.
12. What comes before 100?
101
102
99
98
Correct Answer: 99
99 is the predecessor of 100.
13. What comes after -1 on a number line?
0
-2
1
-5
Correct Answer: 0
Numbers increase towards the right.
14. Which set contains only natural numbers?
0,1,2
1,2,3
-1,0,1
1/2,3
Correct Answer: 1,2,3
Natural numbers start from 1.
15. Which is NOT a rational number?
7
1/4
0
π
Correct Answer: π
π is irrational.
16. Which is the successor of 999?
1000
998
100
9999
Correct Answer: 1000
Successor means next number.
17. Which is a whole number but not a natural number?
1
0
2
5
Correct Answer: 0
0 is whole but not natural.
18. Which number is farthest left on the number line?
5
0
-10
3
Correct Answer: -10
Smaller numbers lie left.
19. Which number is neither positive nor negative?
1
-1
5
0
Correct Answer: 0
0 is neutral.
20. Which number contains an imaginary part?
5 + i
5
1/2
√2
Correct Answer: 5 + i
i represents imaginary unit.
21. Which is an irrational number?
3/5
√3
7
0
Correct Answer: √3
√3 cannot be written as p/q.
22. Which of the following is NOT real?
5
√2
√-1
0
Correct Answer: √-1
√-1 is imaginary.
23. Which number is positive?
9
-9
0
-1
Correct Answer: 9
Positive numbers are greater than 0.
24. Which number is NOT irrational?
π
√11
√13
2/3
Correct Answer: 2/3
2/3 is rational.
25. Which is the predecessor of 1?
1
0
2
-2
Correct Answer: 0
0 comes before 1.
26. Which set contains all real numbers?
R
N
W
Z
Correct Answer: R
R denotes real numbers.
27. Which is NOT a counting number?
1
5
0
9
Correct Answer: 0
Counting numbers begin from 1.
28. Which is the greatest integer?
100
1000
100000
No greatest integer
Correct Answer: No greatest integer
Integers extend infinitely.
29. Which symbol represents imaginary unit?
i
r
n
z
Correct Answer: i
i = √-1
30. Which number system includes all rational and irrational numbers?
Integers
Real Numbers
Whole Numbers
Natural Numbers
Correct Answer: Real Numbers
Real numbers contain rational and irrational numbers.
Submit
Retry
Score
Advanced Number System Interactive Learning
Interactive Number Concepts Learning
15. Even Numbers
Even numbers are numbers divisible by 2.
2, 4, 6, 8, 10...
Example:
24 is even because 24 ÷ 2 = 12
16. Odd Numbers
Odd numbers are not divisible by 2.
1,3,5,7,9...
Example:
15 is odd because it leaves remainder 1 when divided by 2.
17. Prime Numbers
Prime numbers have exactly two factors.
2,3,5,7,11...
Example:
7 has only 1 and 7 as factors.
18. Composite Numbers
Composite numbers have more than two factors.
Example:
12 has factors 1,2,3,4,6,12
19. Co-prime Numbers
Two numbers having only 1 as common factor are co-prime.
Example:
8 and 15 are co-prime numbers.
20. Twin Prime Numbers
Prime numbers differing by 2 are twin primes.
Example:
5 and 7
11 and 13
21. Factors and Multiples
Factors divide numbers exactly.
Multiples are products of numbers.
Factors of 12:
1,2,3,4,6,12
Multiples of 5:
5,10,15,20...
22. HCF
HCF is the greatest common factor.
Factors of 18:
1,2,3,6,9,18
Factors of 24:
1,2,3,4,6,8,12,24
HCF = 6
23. LCM
LCM is the smallest common multiple.
Multiples of 4:
4,8,12,16...
Multiples of 6:
6,12,18...
LCM = 12
24. Successor and Predecessor
Successor means next number.
Predecessor means previous number.
Successor of 99 = 100
Predecessor of 99 = 98
25. Ascending and Descending Order
Ascending = smallest to largest.
Descending = largest to smallest.
Ascending:
2,5,8,10
Descending:
10,8,5,2
26. Place Value
Value of digit according to its place.
In 456:
4 → 400
5 → 50
6 → 6
27. Face Value
Face value is the digit itself.
In 456:
Face value of 5 = 5
28. Expanded Form
Writing numbers according to place values.
456 = 400 + 50 + 6
29. Standard Form
Writing number in usual way.
400 + 50 + 6 = 456
30. Comparing Numbers
Compare numbers using >, < and =
45 > 23
12 < 50
20 = 20
Interactive Quiz (35 Questions)
1. Which is an even number?
24
15
37
99
Correct Answer: 24
24 is divisible by 2.
2. Which is a prime number?
12
21
13
15
Correct Answer: 13
13 has only two factors.
3. Which pair are twin primes?
9 and 11
11 and 13
15 and 17
21 and 23
Correct Answer: 11 and 13
Difference between them is 2.
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Submit
Retry
Score
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