Difference Between Numbers, Numerals, and Digits with Examples
A number can be defined as an arithmetic value used for representing the quantity and is used in making calculations. We count things using numbers. For example, in the image given below, this is one butterfly and these are 4 butterflies.
The collection of no objects in an element is symbolised as '0' and we call it zero. Digits are used to represent numbers, which include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For denoting a number we use a group of digits known as numerals. For example, 1234 2314 56111 are numerals. The method of expressing numbers in words is known as numeration. A number system is defined as a writing system for denoting numbers using digits or using symbols in a logical manner.
The numeral system is used to:
Represents a useful set of different numbers.
Reflects the arithmetic as well as the algebraic structure of a number.
The numeral system provides a standard representation.
One-Digit Numbers
Examples of one-digit numbers are 1, 2, 3, 4, 5,6,7,8, and 9.
Two Digits Numbers
When we add one unit to the greatest one-digit number, we get the smallest two-digit number, which is 1+9 = 10. The greatest two-digit number is 99.
Three-Digit Numbers
When we add one unit to the greatest two-digit number then we get the smallest three-digit number, which is 1+99 = 100. The greatest three-digit number is 999.
Four-Digit Numbers
When we add one unit to the greatest three-digit number, we get the smallest four-digit number that is, 1+999 = 1000. The smallest four-digit number is 1000 and the greatest number is 9999.
Five-Digit Numbers
When we add one unit to the greatest four-digit number, we get the smallest five-digit number, which is 1+ 9999 = 10000. The smallest five-digit number is 10000 and the greatest five-digit number is equal to 99999.
Types of Numbers
The numbers can be classified into sets, which is known as the number system. The different types of numbers in maths are:
Natural Numbers
Natural numbers are also known as counting numbers that contain positive integers from 1 to infinity. The set of natural numbers is denoted as “N” and it includes N = {1, 2, 3, 4, 5, ……….} For example 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Prime Numbers
Prime numbers are natural numbers that are greater than 1 and have only 1 and themselves as factors. For example 2, 3, 5, 7, 11, 13… and so on.
Composite Numbers
A composite number is a natural number that is greater than 1 and has more factors including one. For example 2,4,6,8,9… and so on.
Whole Numbers
Whole numbers are the set of natural numbers in which zero is adjoined. They are known as non-negative integers and it does not include any fractional or decimal part. It is denoted as “W” and the set of whole numbers includes W = {0,1, 2, 3, 4, 5, ……….} For example 0, 1, 2, 3, 4, 5, 6, 7… and so on.
Integers
Integers are the set of all whole numbers but it includes a negative set of natural numbers also. “Z” represents integers and the set of integers are Z = { -3, -2, -1, 0, 1, 2, 3}
They are whole numbers with negative numbers adjoined. For example -9, -8, -7, -6… and so on.
Real Numbers
All the positive and negative integers, fractional and decimal numbers without imaginary numbers are called real numbers. They are denoted by the symbol R. Real numbers are the set of rational numbers with a set of irrational adjoins. For example- 3, 0, 1.5, √2, etc.
Rational Numbers
Any number that can be written as a ratio of one number over another number is written as a rational number. This means that any number that can be written in the form of p/q is a rational number. The symbol “Q” represents a rational number. They can also be defined as fractions with integers. For example ⅔, ⅚, etc.
Irrational Numbers
The number that cannot be expressed as the ratio of one over another or that cannot be written as fractions is known as irrational number, and it is represented by the symbol ”P”. For example √3,√5,√7, etc.
Complex Numbers
The number that can be written in the form of a+bi, where the variables “a and b” are the real numbers and variable “i” is an imaginary number, is known as complex number and is denoted by the letter “C”. For example- 2+3i, 5+2i, etc.
Imaginary Numbers
The imaginary numbers are known to be complex numbers that can be written in the form of the product of a real number and such numbers are denoted by the letter “i”.
What is the Indian Numeral System?
Let us consider a number, say 225. Notice that the digit 2 is used twice in this given number, however, both of them have different values. We differentiate them by stating their place value in mathematics, which is defined as the numerical value of a digit on the basis of its position in any given number. So, the place value of the leftmost 2 is Hundreds while for the 2 in the centre is Tens.
Coming back to the Indian numeral system, the place values of the various digits go in the sequence of:
Ones
Tens
Hundreds
Thousands
Ten Thousand
Lakhs
Ten Lakhs
Crores, and so on.
In the given number 10,23,45,678 the place values of each of the digits present in the number are given below:
We will begin from the right side of the number.
8 – Ones
7 – Tens
6 – Hundreds
5 – Thousands
4 – Ten Thousand
3 – Lakhs
2 – Ten Lakhs
0 – Crores
1 – Ten Crores
The relationship between them is given below:
1 hundred = 10 tens
1 thousand = 10 hundreds = 100 tens
1 lakh = 100 thousands = 1000 hundreds
1 crore = 100 lakhs = 10,000 thousands
International Numeral System
The place values of digits is in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Ten Million and so on, in the international numeral system. In the given number 12,345,678 the place values of each digit is:
8 – Ones
7 – Tens
6 – Hundreds
5 – Thousands
4 – Ten Thousand
3 – Hundred Thousand
2 – Millions
1 – Ten Million
The relations between them are:
1 hundred = 10 tens
1 thousand = 10 hundreds = 100 tens
1 million = 1000 thousand
1 billion = 1000 millions
FAQs on Numbers, Numerals, and Digits Explained for Students
1. What is the name of 0 1 2 3 4 5 6 7 8 9?
The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are known as Arabic numerals. These are also commonly referred to as digits in the decimal number system, which is the standard system used globally for writing numbers. At Vedantu, we teach students how to use these digits effectively as the foundation for all mathematical concepts.
2. Is 2 a number or a digit?
2 is both a digit and a number depending on its usage. As a single symbol in the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 2 is a digit. When it represents a unique quantity or value, it is called a number. In Vedantu's math classes, students learn to distinguish between digits (the building blocks) and numbers (quantities or values).
3. What is the difference between digits and numbers?
Digits are the basic symbols used to form numbers, while numbers are made up of one or more digits to represent a quantity or value. For example:
- A digit: 7
- A two-digit number: 42 (composed of digits 4 and 2)
4. What is a numeral in numbers?
A numeral is a symbol or a group of symbols used to represent a number. Numerals can be written in many forms, such as Hindu-Arabic numerals (e.g., 15), Roman numerals (e.g., XV), or words (e.g., fifteen). At Vedantu, we guide students in identifying and writing numerals in different systems, making mathematical learning comprehensive and engaging.
5. How many digits are there in the decimal number system?
The decimal number system consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These digits are combined in various ways to form all other numbers. Vedantu's learning resources help students efficiently use these digits in solving mathematical problems and understanding advanced concepts.
6. What is the difference between a numeral, a digit, and a number?
Digit is a single symbol (like 3), numeral is a representation of a number using one or more digits (like 23), and number is the mathematical concept or quantity that the numeral expresses. For example:
- The digit: 5
- The numeral: 17
- The number: The actual value or amount expressed, such as seventeen objects
7. Why are digits important in mathematics?
Digits are essential in mathematics because they are the basic building blocks for all numbers. By combining digits, we create larger numbers, perform calculations, and solve complex problems. Vedantu supports students in mastering digit recognition and manipulation, which underpins all areas of math learning and problem-solving.
8. What is the role of numerals in different number systems?
Numerals represent numbers in different numbering systems such as the hexadecimal, binary, or decimal systems. For example:
- Decimal: 25
- Binary: 11001
- Roman: XXV
9. How can Vedantu help students understand numbers, numerals, and digits?
Vedantu provides interactive online lessons, practice exercises, and personalized tutoring to help students thoroughly understand the concepts of numbers, numerals, and digits. Our expert teachers simplify complex ideas and ensure that every student gains a strong mathematical foundation for future learning and exams.
10. How are numbers, numerals, and digits used in daily life?
In everyday life, digits are combined to form numerals that represent numbers used in counting, measuring, timekeeping, and financial transactions. Understanding these concepts is crucial for practical activities such as reading dates, handling money, or measuring quantities. Vedantu bridges the gap between mathematical theory and real-world applications through engaging lessons and relatable examples.
