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# Digit|Definition & Meaning

## Definition

In mathematics, digits are single numbers that are used to represent values. In math, the numbers 0 to 9 are used in various combinations and repetitions to represent all of the values. A digit is a symbol that can represent any of these ten numbers 0 to 9. 24 is an example of a two-digit (2-D) number. It is made up of the numbers 2 and 4.

## Digit

The digits in the **binary number system** are the elements of the set **0 and 1.** Computers use this system because the **low and high logic** states can be represented by **two digits**.

In computer jargon, the term “**binary digit**” is abbreviated to “**bit**”. The** octal and hexadecimal** numbering systems are also used in computing. The digits in the o**ctal number system** are the set’s elements **0, 1, 2, 3, 4, 5, 6, 7**. The elements in the set **0, 1, 2, 3, 4, 5, 6, 7, 8, 9 A, B, C, D, E, and F** make up the digits in the hexadecimal system.

The term “**digit**” is frequently used to denote a number in a specific position within a larger number, a number that uses** radix points** to express a fraction.

In the decimal number **2609**. For example, the number **2** represents the** thousands digit**, the number **6** represents the** hundreds digit**, the number **0** represents the **tens digit**, the number **9** represents the **ones digit**, and in numeral 37 the number** 3** represents the** tenths digit, t**he hundredth digit is represented by the number 7.

The term digit refers to a human or animal’s finger or toe in biology and anatomy. Any tiny, practical appendage in a robotic end effector may be referred to by this term.

## History of Digits

When the number system was unknown thousands of years ago, people used stone tokens or **Roman abacuses**. The need for larger denominations was felt as time passed and trade across regions and countries advanced. As a result, number systems as we know them today were developed.

As nations advanced, so did the need to deal with larger populations. The size of a microorganism, the distance between the** Earth and the Moon, and the speed of light**; these enthralling facts instilled in us the desire to expand our number systems. As a result, the concept of numbers and digits was introduced.

Counting small numbers is simple. We can count the petals of a flower and the fingers on our hands without the use of a calculator or a pen and paper. In such cases, we deal with single-digit numbers. The smallest single-digit counting number is one, and the greatest is nine.

Consider the students in your class. Can you easily count them? A small class of forty to eighty students might get a yes. Similarly, for counting the number of buildings in a neighborhood, the number of general stores in a neighborhood, and so on. We use numbers up to two digits to keep track of such measures.

## Numbers With Two Digits

We get the smallest** two-digit** number by adding one unit to the greatest **one-digit number**.** 1 + 9 = 10 **

The smallest two-digit number is** ten**, and the greatest is **ninety-nine**.

Consider an auditorium with hundreds of people. We can’t possibly count this many people with our fingertips. We use numbers up to three digits to deal with such measures.

## Numbers With Three Digits

We get the smallest **three-digit number** by adding one unit to the greatest **two-digit number**.

**1 + 99 = 100**

**100** is the **smallest three-digit number**, and the g**reatest three-digit number is 999**.

Consider the crowd in a sports pavilion, which could number in the thousands. For example, to deal with the cost of a cupboard or a bicycle, we use digits up to four digits.

## Numbers With Four Digits

We get the **smallest four-digit number by adding one unit** to the** greatest three-digit number.**

** 1 + 999 = 1000**

**1000 is the smallest four-digit number, and 9999 is the largest.**

When dealing with numbers as large as a state’s population or the cost of a motorcycle, we must deal with five-digit figures.

## Numbers With Five Digits

We get the **smallest five-digit number by adding one unit to the greatest four-digit number**.

** 1 + 9999 = 10000 **

**The smallest five-digit number is 10000, while the largest is 99999.**

## Place Value

In mathematics, each digit in a number has a **place value.** Place value is the value that a digit in a number denotes based on where it appears in the number.

For instance, the place value of **4 in 5465 is 400 hundreds**. The place value of** 4 in 4652**, on the other hand, is** 4 thousands or 4000**. We can see here that, even though the **4** is the same in both numbers, its place value changes as its position changes.

## Face Value

**Face value** and place value are not synonymous. The face value of a digit is its value, whereas the place value of a digit is its **position in the number**. Simply put, the **face value represents the actual value**, whereas the place value represents the value based on its position.

As a result, the digit’s face value remains constant regardless of its position in the number, whereas its place value changes as its position changes.

Taking the face value of **4** as an example in both** 264 and 545 is 4**. Whereas **4 **has a place value of **400 in 264 and 40 in 545**.

## Examples of Digits in Problems

### Example 1

In 6587, how many digits are there?

### Solution

The number of digits in 6587 is 4, which are 6, 5, 8, and 7.

### Example 2

Find the greatest three-digit number using the digits 9, 5, and 9.

### Solution

The greatest three-digit number that can be formed using these is 995.

### Example 3

In the number 65,847, what is the place value of the digit 5?

### Solution

The place value of 5 in 65,847 is 5000 or five thousand.

### Example 4

What are the smallest and greatest four digits in 1,0,0,0?

### Solution

1000 is the smallest four-digit number.

9999 is the largest four-digit number.

*All images/mathematical drawings were created with GeoGebra.*