The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Numbers are omnipresent, as they are fundamental topics that constitute the subjects of maths, physics, and chemistry. Numbers are the first things that we learn in our initial stages of our learning journey. They are classified into different types and kinds. You must have heard of odd and even numbers. Similarly, there are many types of numbers and numerous operations that we can perform on them. Before building the fortress of maths, let’s check the base of **knowing our numbers**.

Any mathematical object used to count, measure, and put abstract things in measurable format is a number. The basic counting consists of 10 numbers, from 0 to 9. These are 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers form the base of counting and other mathematical operations.

**Introduction to Comparing Numbers**

We have so many numbers it is impossible to count. Positive numbers start from zero and go till infinity. However, there are many rules for comparing numbers. Let’s check some of those rules below:

**Rule 1**: Whichever number has more place values is greater. Suppose we take two numbers, 23 and 783. The 23 has place values up to tens, but 783 has place values up to hundreds, and hence 783 is larger than 23. But what if both the numbers have the same number of digits. How can we calculate which is greater at that time?

**Rule 2**: If both the numbers have the same number of digits, then we start comparing the digits of both from the highest place value till the one’s place. For example, if we have two numbers 245 and 225. In this, we start from hundreds of places and find that both are the same as 2. Now we go to the tens place and find that 4 is greater than 2. Hence 245 is greater than 225.

There can be two numbering orders based on the size of the numbers:

**Ascending Order:** When the number series has the smallest number initially, and the last number of that series is the highest, then we have the numbers in ascending order. The left number is always smaller or equal to the number on the adjacent right in ascending order.

**Descending Order:** When a series of numbers is formed in a manner that the first number is the highest and the last number is the smallest, then we have a descending order. In descending order series, the right number is always smaller than the left adjacent number. You can try these small and **large numbers in practice** for rearranging numbers.

For example, convert the data set of 34, 54, 22, 77, 64, 98, 23 and 12 in ascending and descending order.

According to the above definition, the ascending order is as follows:

12, 22, 23, 34, 54, 64, 77, 98

And the descending order would be:

98, 77, 64, 54, 34, 23, 22, 12

The basic purpose of commas in number systems is to ease the reading of numbers and their understanding. In the Indian system of numeration, we put commas at hundreds, ten thousand, ten lakhs, ten crores, and so on. The first comma is put after the three digits, and then comma comes after every two digits. For examples, check these numbers.

23,345

345

2,345

1,23,24,234

We can separate these examples **using brackets**. When we have multiple numbers, brackets are a good tool to separate them clearly.

In the Roman form of number representation, we use a mix of Latin alphabets and numbers. Some of the Roman numbers are given below:

1 I2 II3 III4 IV5 V6 VI7 VII8 VIII9 IX10 X

**Knowing Our Numbers** is an important chapter in maths NCERT since numbers can be found anywhere with various applications. For each profession, numbers mean different things. We can play with numbers by performing various operations and categorising them into certain categories based on any predefined definition. When we see clocks, the profit & losses of any business, the number of cakes that you want to eat are all specified with certain numbers.

**What is playing with the numbers?**

Playing with numbers is an NCERT maths chapter that deals with the basics of mathematics. It introduces the concept of numbers and their different properties.

**How can numbers be arranged?**

Whenever we are given raw data sets containing numbers, it contains those numbers in unarranged form. To make things simple for understanding, we can simplify and arrange them in two patterns. One is ascending order, and the other is descending order.

**Why are roman numerals used?**

A Roman numeral is a Latin form of number system that is used from conventional times. It has been used for centuries and hence is continuing now also for aesthetics.

**How many numbers are there?**

On a number line, we can represent numbers, and there are infinite numbers. If we start from zero, we can have both positive numbers and negative numbers until infinity.

**Why are commas used in the numerical system?**

Commas are meant to simplify the numerical understanding process. The first comma is put after the three digits at hundred places. After that, commas are put after every two digits to separate thousands, lakhs, crores and more.

**What operations can be performed on numbers?**

We can perform various operations on numbers such as addition, subtraction, multiplication and division.

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