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Types of Numbers
What are Types of Numbers?
Types of numbers are different sets of numerical values.
To determine the type of number, you must use the definition to see whether the number belongs to the set.
Understand number definitions and terms
A number is a count or measurement.
We write or talk about numbers using numerals such as '6'. We need to know the different types of numbers to be able to solve problems.
- Positive and negative numbers
Any number above zero is a positive number and any number below zero is a negative number.
- Real Numbers
All numbers on a number line are real numbers.
Real numbers can also be classified as rational or irrational. - Rational and irrational numbers
We can make a rational number by dividing an integer by an integer.
Irrational numbers are the real numbers that cannot be expressed in fraction form. - Natural numbers are positive integers (including 00). We can also call these 'counting' numbers'.
For example,
- Even and odd
Even numbers are divisible by 2 without remainders; they end in 2, 4, 6 or 8.
Odd numbers are not divisible by 2 without remainders and end in 1, 3, 5, 7 or 9.
For example,
- Decimals
We can recognise decimal numbers because they have a whole number and a fractional part. The decimal point separates the whole number from the fractional part.
For example,
- Prime numbers and composite numbers
A prime number is a number which is only divisible by 1 and itself. We can define composite numbers as whole numbers that have more than two factors.
For example,
3 = 3 × 1, so 3 is prime.
6 = 3 × 2, or 6 = 1 × 6. 6 has more than two factors, so 6 is composite.
We also need to recognise the properties of some other 'special' numbers. - Square numbers
Square numbers are the product of a number that has been multiplied by itself.
We can show square numbers using a pattern of dots in a square.
For example,
- Cube numbers
A Cube number is the product when a number has been multiplied by itself twice. We can show cube numbers using 3D cubes.
For example,
- Triangular numbers
A Triangular number is a number that can be shown using a pattern of dots in an equilateral triangle. We can find a triangular number by cumulatively adding natural numbers.
For example,
- Reciprocal maths
A reciprocal of a number is its multiplicative inverse. This means that if you multiply a number by its reciprocal the answer is 1.
To find a reciprocal you divide 11 by the number.
For example, the reciprocal of 3 is 1/3
Key Types of Number
Below is a description of each of these types of numbers, along with a few examples.
Other Types of Number
Fractions and Decimals
There are also a few specific types of numbers involving fractions and decimals that you are expected to understand. Below is a table outlining these different types of fractions and decimals.
The document Types of Numbers is a part of the Grade 10 Course Mathematics for Grade 10.
All you need of Grade 10 at this link: Grade 10
FAQs on Types of Numbers
| 1. What's the difference between rational and irrational numbers? |  |
Ans. Rational numbers can be expressed as fractions (p/q) where both p and q are integers, like 3/4 or 5. Irrational numbers cannot be written as fractions and have non-repeating, non-terminating decimals, such as π and √2. Together, they form the real number system studied in CBSE Grade 10 mathematics.
| 2. How do I identify if a number is prime or composite in an exam? | |
Ans. A prime number has exactly two factors: 1 and itself (2, 3, 5, 7, 11). A composite number has more than two factors (4, 6, 8, 9, 12). To check quickly, test divisibility by small primes up to the square root of the number. Note: 1 is neither prime nor composite-this distinction is crucial for Grade 10 exams.
| 3. Why do we call some decimals repeating and others terminating? | |
Ans. Terminating decimals end after a finite number of digits (0.5, 0.75), occurring when denominators have only factors of 2 and 5. Repeating decimals continue infinitely with a pattern (0.333... or 0.142857...), appearing when denominators have prime factors other than 2 or 5. Both types represent rational numbers in decimal form.
| 4. What exactly are whole numbers, and how are they different from natural numbers? | |
Ans. Natural numbers are counting numbers starting from 1 (1, 2, 3, 4...), while whole numbers include 0 plus all natural numbers (0, 1, 2, 3, 4...). This distinction matters in CBSE mathematics-whole numbers form a superset. Both are subsets of integers, which also include negative numbers.
| 5. How do perfect squares and perfect cubes relate to number types in Grade 10? | |
Ans. Perfect squares result from multiplying an integer by itself (4, 9, 16, 25), while perfect cubes come from multiplying an integer three times (8, 27, 64, 125). Both are rational numbers that appear frequently in exam problems about number classification, surds, and simplification of irrational expressions involving roots.
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