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 main difference between a number, a numeral, and a digit?
The difference is key to understanding maths. A digit is a single symbol used to make numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). A numeral is the written representation of a number, like '25' or 'IX'. A number is the actual idea or quantity itself. For example, the idea of 'ten' is a number, while '10' and 'X' are the numerals we write to represent it.
2. What do 'place value' and 'face value' of a digit mean in a numeral?
Both terms describe a digit's value within a numeral, but in different ways:
- Face Value: This is the digit's individual value, regardless of its position. In the numeral 742, the face value of '4' is simply 4.
- Place Value: This is the value a digit holds based on its position (ones, tens, hundreds, etc.). In 742, the place value of '4' is 40 (4 x 10) because it is in the tens place.
3. How does the position of a digit change its value in a number? Explain with the numeral 333.
The position of a digit is crucial in a positional number system like the one we use. In the numeral 333, all three digits have a face value of 3, but their place values are completely different:
- The rightmost '3' is in the ones place, so its value is 3 (3 × 1).
- The middle '3' is in the tens place, making its value 30 (3 × 10).
- The leftmost '3' is in the hundreds place, giving it a value of 300 (3 × 100).
4. What is the difference between the Indian and International systems of numeration?
The main difference is in the placement of commas and the names given to larger place values.
- Indian System: Commas are placed after the first three digits from the right, and then after every two digits. The place values are named Ones, Tens, Hundreds, Thousands, Lakhs, Crores. Example: 5,43,21,000 (Five crore, forty-three lakh, twenty-one thousand).
- International System: Commas are placed after every three digits from the right. The place values are named Ones, Tens, Hundreds, Thousands, Millions, Billions. Example: 54,321,000 (Fifty-four million, three hundred twenty-one thousand).
5. Why is zero (0) considered such an important digit?
Zero is a fundamental concept in mathematics for two primary reasons:
- It is a number: Zero represents the quantity of 'nothing' or an empty set. It is the starting point on the number line.
- It is a placeholder: This is its most powerful role in numerals. Without zero, we couldn't differentiate between 51, 501, and 5001. The '0' holds the place to ensure other digits are in their correct positions (tens, hundreds, etc.), which gives our number system its power and clarity.
6. Where can we see examples of numbers and numerals used in our daily life?
We use numbers and numerals constantly in our daily lives. Some common examples include:
- Reading the time on a clock.
- Checking the date on a calendar.
- Using money to buy things (prices and change).
- Dialling a phone number.
- Finding a page number in a book.
- Measuring ingredients for a recipe.
- Checking the speed of a car on the speedometer.
7. How do you write the number 'Seventy-two thousand, five hundred six' as a numeral?
To write this as a numeral, you break it down by place value:
- 'Seventy-two thousand' is written as 72,000.
- 'Five hundred' is written as 500.
- 'Six' is written as 6.
8. What are Roman numerals and what are their basic symbols?
Roman numerals are an ancient numbering system that uses letters of the alphabet to represent numbers. Unlike our system, it is not a fully positional system. The seven basic symbols and their values are:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1,000
