## What Are Numerals?

**Numerals are symbols or signs (or collection of symbols) used to represent numbers corresponding to numerical quantities, values, or measurements.**

Numerals often come together with a set of rules for representing larger numbers. They provide a concise and standardized way to express numerical quantities.

Numerals help us communicate numeric values or numerical quantities effectively. In math, a number conveys a quantity. You can say that a number offers an answer to the question “how many things are there?.” A numeral helps us to write it down.

**Example 1:** If you have 3 apples, you can use different numerals to represent this quantity.

- Number: 3
- Number name: Three
- Roman numeral: III
- Symbol/Sign (using dots): ●●●

**Example 2:** Take a look at the image given below. What do you see?

This image shows two cups, two soccer balls, and two ice cream cones. Here, “two” indicates a quantity. We can represent this quantity using different numerals, such as

- Number: 2
- Word form: Two
- Roman numerals: II
- Using dots: ●●

So, each of these is a numeral representing the quantity “two.”

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## Numerals: Definition

A numeral is a symbol or a sign that stands for a number. A numeral can be defined as a representation of a number, which can be in the form of a figure, symbol, name, or a combination of figures and symbols.

**Example**: Seven, VII, ७, etc. are all symbols or signs we use to indicate the number “7.”

Each one of them is a numeral.

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## Numbers vs. Numerals

The terms “numbers” and “numerals” can be confusing. The concept of a number is distinct from its written representation, which is the numeral. Let’s understand the difference.

Numbers | Numerals |
---|---|

A number is an idea or an abstract mathematical concept that represents a quantity. | A numeral is a way to write and represent this quantity. It is a written or symbolic representation of numbers. |

We can express a number in many ways with the help of numerals. | Each numeral represents a single number. |

Example: We can write the number 6 as Six, VI, or VI. | Example: Six, VI, or VI are numerals representing the same number 6. |

## What Are Different Numeral Systems?

A numeral system is a way to represent numbers. Numeral systems, also known as number systems, indeed consist of symbols and rules for representing numbers and quantities. They play a crucial role in mathematics and are used to express numerical values in a standardized and systematic manner.

There are many ways to represent a number with the help of symbols in math. In other words, we can represent a number using more than one numeral.

Note that many numeral systems have evolved across various regions and cultures, each serving a distinct purpose. Let’s discuss a few.

**Arabic numerals or Indo-Arabic numerals (Hindu-Arabic numerals):**

Arabic numerals, also known as Indo-Arabic or Hindu-Arabic numerals, are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) we commonly use in our number system. The decimal number system is the extension of the Indo-Arabic numeral system.

**Roman numerals:**

Roman numerals are a numeral system originating from ancient Rome, characterized by the use of letters from the Latin alphabet to represent numbers. Roman numerals are still used today in specific contexts, such as numbering book chapters or indicating the date on clock faces.

I (1), II (2), V (5), X (10), L (50), C (100), D (500), M (1000), etc.

**Binary numerals:**

Binary numerals, often referred to as base-2 numerals, are a numeral system that uses only two digits: 0 and 1. It is widely used in computer systems.

Decimal Number | Binary Number |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

**Octal numerals:**

Octal numerals, a base-8 numeral system, use eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.

**Chinese numerals:**

Chinese numerals, also known as Han numerals, are used in the Chinese writing system to represent numbers.

$\bigcirc$ (0), 一 (1), 二 (2), 三 (3), 四 (4), 五 (5), 六 (6), 七 (7), 八 (8), 九 (9), 十 (10)

**Number names or Word form**:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Zero | One | Two | Three | Four | Five | Six | Seven | Eight | Nine |

**Devanagari numerals:**

Devanagari numerals are the numeric symbols used in the Devanagari script, primarily in the Indian subcontinent. They are the scripts used for languages like Sanskrit, Hindi, Marathi, and Nepali.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

० | १ | २ | ३ | ४ | ५ | ६ | ७ | ८ | ९ |

Tally marks are a simple system of counting and recording numbers using vertical lines or strokes, in sets of 5. Each group of five tally marks is typically represented by four vertical lines, with the fifth line being drawn diagonally across the previous four.

## What Is the Decimal Numeral System?

The decimal numeral system is the most commonly used number system. This system is also known as the base-10 positional numeral system since it used 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to form all the numbers. It is derived from the Indo-Arabic numeral system.

Decimal numerals (often called simply as decimals refers to the notation of a number. In this system, the integer portion and the decimal portion of a numeral are separated using a decimal point.

**What Are Place Values?**

Place value refers to the value of a digit in a number by the virtue of the position in the number. The place values of digits in the decimal system are represented using the powers of 10. In decimal numbers, the whole number part and the fractional part is separated by the decimal point.

In the international place value chart, there are three periods for the nine places from right to left. Each period has three place values.

## Facts about Numerals

- Numerals are symbols used to represent numbers. Different numeral systems are used worldwide, reflecting cultural and historical diversity.
- The Roman numeral system indeed did not have a symbol for zero.
- The ancient Egyptians made significant contributions to the development of numerals and mathematical systems.
- The earliest numerals used by humans were simple scratches on a rock or stone, notches on a stick, etc.

## Conclusion

In this article, we learned about numerals. We explored a few commonly known numeral systems as well. To deepen our understanding, let’s dive into practical examples and MCQs for enhanced comprehension.

## Solved Examples on Numerals

**Example 1: What is the word form for 42?**

**Solution**:

The word form for the number 42 is “Forty Two.”

**Example 2: How many candies are there in the bowl? Represent the numerical quantity using different numerals.**

**Solution**:

There are 9 candies in the bowl.

**Example 3: What is the time shown in the given analog clock?**

**Solution**:

The hour hand points exactly to V, which is the roman numeral for 5.

The minute hand points exactly to XII, which is the roman numeral for 12.

So, the clock reads 5 o’clock.** **

## Practice Problems on Numerals

## Numerals - Definition, Numeral Systems, Facts, Examples, FAQs

### What is the roman numeral for 4?

4 = IV

### Which of the following is not a numeral for 1?

The last option does not represent the number 1.

It either represents the number “thousand,” or the binary number equivalent to 8.

### In the decimal numeral system, the base is ____.

The decimal numeral system is a base-10 number system.

### Identify the numeral of 7.

7 = Seven in word form = Ⅶ in Roman numerals

## Frequently Asked Questions about Numerals

**What are digits in math?**

A digit is a single numerical symbol used to represent numbers. A number is a mathematical concept or idea used to represent a quantity.

**What is the difference between a numeral and a digit?**

A numeral is a symbol or group of symbols used to represent a number, either using digits, words, other signs and symbols, etc.

**What is the difference between digits, numbers, and numerals?**

Number is expressed with digits, while a numeral is how we describe a number.

**What is the place value of a digit?**

The place value of a digit indicates its position in a number. For example, in 36, the place value of 3 is 30, while that of 6 is 6.

**Are all numeral systems based on place values?**

No, all numeral systems are not based on place values. For instance, the Roman numeral system is not based on place values.