Numbers, Numerals and Digits

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What are Numbers?

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We count things using numbers.

For example, in the image given below this is one butterfly and these are 4 butterflies.

this is one butterfly and these are 4 butterflies


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, that is 1+9 = 10

The smallest two-digit number is 10 and the greatest one is 99.

Two Digits Numbers


Three Digit Numbers

When we add one unit to the greatest two-digit number then we get the smallest three-digit number, that is 1+99 equals 100

The smallest three-digit number is 100 and the greatest number is 999.

Three-Digit Numbers

 

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 equal to 1000

The smallest four-digit number is 1000 and the greatest number is 9999.

 

Four Digit Numbers


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.

Five Digit Numbers

The smallest five-digit number is 10000 and the greatest five-digit number is equal to 99999.

 

What are Numbers? 

A number can be defined as an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is called numerals. 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

Types of Numbers

The numbers can be classified into sets 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 the positive integers from 1 to infinity. The set of natural numbers is denoted as “N” and it includes N = {1, 2, 3, 4, 5, ……….}

  • Whole Numbers: 

Whole numbers 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, ……….}

  • 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}

  • 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.

  • Rational Numbers: 

Any number that can be written as a ratio of one number over another number is written as rational numbers. This means that any number that can be written in the form of p/q. The symbol “Q” represents the rational number.

  • Irrational Numbers: 

The number that cannot be expressed as the ratio of one over another is known as irrational numbers, and it is represented by the symbol ”P”.

  • 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 numbers and is denoted by the letter “C”.

  • Imaginary Numbers: 

The imaginary numbers are known to be the 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. 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 center is Tens.

Coming back to the Indian numeral system, the place values of the various digits go in the sequence of 

  1. Ones

  2. Tens

  3. Hundreds

  4. Thousands

  5. Ten Thousand

  6. Lakhs

  7. Ten Lakhs

  8. 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 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 equals 10 tens

  • 1 thousand equals 10 hundreds equals 100 tens

  • 1 lakh equals100 thousands equals 1000 hundreds

  • 1 crore equals 100 lakhs equals 10,000 thousands

International Numeral System

The place values of digits go in the given 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 are:

  • 8 – Ones

  • 7 – Tens

  • 6 – Hundreds

  • 5 – Thousands

  • 4 – Ten Thousand

  • 3 – Hundred Thousands

  • 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

FAQ (Frequently Asked Questions)

Question 1. What is a Numeral in Math?

Answer: A numeral can be defined as a figure, symbol, or group of figures or symbols which denote a number. The numeral system is commonly used in mathematics. Numeral (linguistics), is known to be a part of speech denoting numbers (e.g. one and first in English) Numerical digit, are used to represent numerals.

Question 2. How Many Digits are Used to Form Numerals?

Answer: Ten digits.  A digit can be defined as a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the ten digits that are used in everyday numerals.

Question 3. What are Basic Numerals?

Answer: The numbers used in our day to day life can be expressed by the following digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Thus, we can regard 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 as basic numerals.

Question 4. What is a Numeric Number?

Answer: Numeric is anything of, relating to, or containing numbers. The numbering system consists of ten different digits they are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If a value is alphanumeric, it contains letters and numbers.

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