What Are Numbers?
In math, numbers can be even and odd numbers, prime and composite numbers, decimals, fractions, rational and irrational numbers, natural numbers, integers, real numbers, rational numbers, irrational numbers, and whole numbers. How do you define a number? You can define a number as a count, like in a race, when we say, 3, 2, 1, GO!” or a measurement such as John Cena weighs 275 lbs. There are also fractions such as 22/7 and decimals such as 3.14. Numbers are an integral part of our everyday lives, right from the number of hours we sleep at night to the number of rounds we run around the racing track. Numbers define world records, sales, miles - you name it, and it has a number. In this chapter, we'll give you an introduction to the different types of numbers that are in math and those we use.
| 1. | Numbers and Number Names |
| 2. | Types of Numbers |
| 3. | Solved Examples on What Are Numbers |
| 4. | Practice Questions on What are Numbers |
| 5. | FAQs on What Are Numbers |
Numbers and Number Names
Numbers are the origin of mathematics and without numbers math is nothing. Number name is referred to the pattern of writing a number in words. For example 1 in words is written as one. Let us have a look at some numbers and their number names.
0 = Zero, 1 = One, 2 = Two, 3 = Three, 4 = Four, 5 = Five, 6 = Six, 7 = Seven, 8 = Eight, 9 = Nine.
The above mentioned numbers are the basic numbers with the help of which we can form 2-digit, 3-digit, 4 digit, n-digit numbers. To write a larger numbers in words or vice-versa it is significant that we know the place value of those numbers.
For Indian place values, places are grouped into four periods - ones, thousands, lakhs, and crores. These four periods has nine place values which are denoted as - Ones [ones, tens, and hundreds], thousands [thousands and ten thousands], lakhs [lakhs and ten lakhs], crores [crores and ten crores]. Let us see how the numbers are represented in International as well as Indian numeration system with the help of this chart given below.
Types of Numbers
Numbers are classified in various forms. Any natural number like 1, 2, 3, etc, is termed as a cardinal number. For counting we use cardinal numbers. Similarly there is another pattern for numbers which is an ordinal number. It is a number that denotes the position of an object. For example: 1st, 2nd, 3rd etc. Mostly for ranking we use ordinal numbers. Numbers are classified into several types like we mentioned above. Let us have a look at some major and important types of numbers which we use often.These include:
- Prime and composite numbers
- Even and odd numbers
- Fractions and decimals
- Rational and irrational numbers
- Natural numbers
- Integers
- Real numbers
- Whole numbers
- Rational Numbers
Natural Numbers
All the counting numbers from 1 to infinity (countless) are called natural numbers.
Whole Numbers
The numbers which start from zero (0) are called whole numbers. In other words, the combination of zero and natural numbers are called whole numbers.
Integers
The positive and negative numbers along with zero are called integers. Zero does not stand for positive or negative. It is neutral in the center. The positive numbers are called positive integers and negative numbers are called negative integers.
Rational Numbers
Any number which is defined in the form of a fraction or ratio is called a rational number. This may consist of the numerator (p) and denominator (q). A rational number can be a whole number or an integer.
Irrational Numbers
Irrational numbers are those in which the fraction or the ratio cannot be determined i.e. it cannot be expressed in the form of a fraction or a ratio. Irrational numbers cannot be expressed in decimal form since the decimal numbers extend continuously and never repeat. For instance, π (pi) is an irrational number because it does not have any decimal pattern and it goes non-terminating.
Real numbers
Real numbers in maths are numbers that include both rational and irrational numbers. Thus rational numbers is a set of all the natural numbers, whole numbers, and integers.
Prime and Composite Numbers
In mathematics, composite numbers are the numbers that have more than two factors, unlike prime numbers, which have only two factors, i.e., one and the number itself. Such numbers with more than two factors also are called composites. The natural numbers greater than one that aren't prime are called composites because they're divisible by more than two numbers. The numbers 0 and 1 are neither prime nor composite, and therefore 2 is the first prime number, and 4, the first composite number.
Meanwhile, prime number is the whole number greater than 1 that has exactly two factors, 1 and itself. Another equivalent definition is: any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number. For example:13 has just two factors:1 and 13. Hence it is a prime number. There are around 25 prime numbers upto 100. They are:
- Prime Numbers between 1 and 10 are 2, 3, 5, 7
- Prime Numbers between 11 and 20 are 11, 13, 17, 19
- Prime Numbers between 21 and 30 are 23, 29
- Prime Numbers between 31 and 40 are 31, 37
- Prime Numbers between 41 and 50 are 41, 43, 47
- Prime numbers between 51 and 100 are 53, 57, 61, 67, 71, 73, 79, 83, 89, 97
Even and Odd Numbers
A number that's divisible by 2 and generates a remainder of 0 when divided by 2 is known as an even number. An odd number is a number that isn't divisible by 2. The remainder within the case of an odd number is 1. An even number can be described as a number that may be divided into two equal groups. An odd number, on the other hand, can't be divided into two equal groups. Even numbers end in 2, 4, 6, 8, and 0, no matter what preceding digits they have. Odd numbers end in 1, 3, 5, 7, and 9, no matter what preceding digits they have. Even numbers are often divided evenly into groups of two. The Number 4 is usually divided into two groups of Numbers of 2(2+2). Even numbers always end with numbers like 0, 2, 4, 6, or 8. All these numbers like 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are even numbers.
Odd numbers can't be divided into two groups. Number 5 is often divided into two groups of two and one group of 1. Odd numbers always end with numbers like 1, 3, 5, 7, or 9. All these numbers like 1, 3, 5, 7, 9, 11, 13, 15, 17,19, 21, 23, 25, 27, 29, 31 are odd numbers.
Decimals and Fractions
A fraction is a part of a whole. The whole itself can be a number, an object, or a group of numbers (or objects). Fractions help us speak of numbers besides whole numbers. For instance, 15 and 16 are whole numbers — but a fraction is needed to write out a number that is between 15 and 16. Decimals help us like fractions do — but are separate entities. This number line shows us a few whole numbers on the number line.
Fractions and decimals both exist on the number line. In fact, every fraction has an equivalent decimal. The real difference between the two is how they are written out.
Index Numbers
Index numbers tell you how many times you have to use the number in a multiplication. Consider the following example:
82 = 8 × 8 = 64
83 = 8 × 8 × 8 = 512
84 = 8 × 8 × 8 × 8 = 4096
Using indices, you can also write large numbers using powers of 10. Scientists use this to calculate large values that go into billions and trillions. For example, the speed of light is 300,000,000 m\s. However, most science textbooks show it as 3 ×108 m\s. This is the best way to use the power of 10. Another example is the mass of the sun. The sun has a mass of 1.988 × 1030 kg. It is easier to write this, than 1,988,000,000,000,000,000,000,000,000,000 kg. Chances are, you may make a mistake counting 30 zeroes!
Important Notes
- The numbers which start from 1 and go up to infinity are called natural numbers.
- The numbers which start from zero are called whole numbers.
- Integers consist of positive and negative numbers along with zero.
- Rational numbers consist of integers, fractions, and ratios.
- Irrational numbers are not expressed in the form of fractions or ratios.
- Real numbers consist of natural numbers, whole numbers, rational numbers, and irrational numbers.
Related Articles on What Are Numbers
FAQs on What Are Numbers
What is the Biggest Number?
People may argue that the largest number is infinite, but we don't have a definite number of zeroes for that number. However, mathematicians have said that the largest number is called googol. It is 1 followed by one hundred zeroes and can be written as 10100.
What are the Basic Numbers?
The numbers 0 to 9 are called the basic numbers.
What is not a Real Number?
Any number that cannot be used in our basic arithmetic operations is called an imaginary number. These imaginary numbers that cannot be represented on the number lines are not real numbers.
What are the First 10 Numbers?
The first 10 counting numbers(natural numbers) are the first ten numbers. These are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
What are the First 25 Prime Numbers?
The first 25 prime numbers are:
- Prime Numbers between 1 and 10 are 2, 3, 5, 7
- Prime Numbers between 11 and 20 are 11, 13, 17, 19
- Prime Numbers between 21 and 30 are 23, 29
- Prime Numbers between 31 and 40 are 31, 37
- Prime Numbers between 41 and 50 are 41, 43, 47
- Prime numbers between 51 and 100 are 53, 57, 61, 67, 71, 73, 79, 83, 89, 97
What are Odd Numbers?
Odd numbers are the numbers which cannot be divided into two groups. Number 5 is often divided into two groups of two and one group of 1. Odd numbers always end with numbers like 1, 3, 5, 7, or 9. All these numbers like 1, 3, 5, 7, 9, 11, 13, 15, 17,19, 21, 23, 25, 27, 29, 31 are odd numbers.