DIGITS AND NUMBERS

​DIGITS AND NUMBERS

​DIGITS AND NUMBERS

• Digits are the individual numbers used for counting and representing quantities. They serve as the building blocks of numbers. When we count or work with numbers, we rely on digits. These small symbols play a crucial role in expressing the value of a number.

• In mathematics, there are ten digits that form the foundation for all numerical representations. These digits are:

• Digits are the single numbers used to represent values in math. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are used in different combinations and repetitions to represent all the values in math. 

  Any of the ten numbers from 0 to 9 can be represented by a symbol known as a digit.

• These numerals combine in various ways to create different numbers. For instance, when you count from 1 to 10, you are using these digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Digits help us express how many things there are or specify a particular position within a number.

​NUMBERS

​ A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as numerals. A number system is a writing system for denoting numbers using digits or symbols in a logical manner. The numeral system:

• Represents a useful set of numbers

• Reflects the arithmetic and algebraic structure of a number

• Provides standard representation

• We use the digits from 0 to 9 to form all other numbers. 

  0

  1

  2

  3

  4

  5

  6

  7

  8

  9

  With the help of these digits, we can create infinite numbers.

​Counting Numbers:

We use numbers to count different things or objects such as 1, 2, 3, 4, etc. Humans have been using numbers to count things from the past thousands of years. For example, there are 7 cows in the field. The counting numbers start from 1 and it goes till infinity.

The Number Zero:

The concept of the number “Zero (0)” place an important role in Mathematics and it is used as a placeholder in the place value number system. The number 0, acts as an additive identity for the real numbers, and other algebraic structures. We use the number “0” to show nothing. For example, there were 3 apples, but now there are none. To represent nothing, we can use zero.

​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 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} (https://en.wikipedia.org/wiki/Integer )

• Real Numbers: All the positive and negative integers, fractional and decimal numbers without imaginary numbers are called real numbers. It is represented 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 “a and b” are the real number and “i” is an imaginary number is known as complex numbers “C”.

• Imaginary Numbers: The imaginary numbers are the complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”

​Place Value

In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

For example, the place value of 7 in 3743 is 7 hundreds or 700. However, the place value of 7 in 7432 is 7 thousands or 7000. Here, we can see that even though the 7 is the same in both numbers, its place value changes with the change in its position. 

​Face Value
Place value and face value are not the same. The face value of a digit  is the value of the digit whereas the place value of a digit is its place in the number. In simple words, the face value tells the actual value whereas the place value tells the value based on its position.  Hence, the face value of the digit never changes irrespective of its position in the number, whereas its place value changes with the change in its position. 
Ex : let the number 2359842
In the above number :
The face value of 9 is 9 only
The place value of 9 is 9000.

Successor and Predecessor

The predecessor is the number that comes just before it
The predecessor is found by subtracting 1: n - 1. 

Predecessor

The successor of a number is the number that comes immediately after it
The successor is found by adding 1: n + 1.

Successor