From rolling the dice for playing a game of snakes and ladders to counting the stars in the universe, everything is a game of numbers. So we must have a complete understanding of numbers. Here we will see the general form of numbers along with how to compare them in descending and ascending order.

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## The Place Value

We have done the concept of place value in earlier classes and might remember the expansion of a two digit number. Let us hit the refresh button and revisit the general forms of numbers.

Let us consider the example of a two digit number- 67. Now when we start from the right i.e from 7 to 6, the place of seven is known as *ones* and that for 6 is known as *tens*.

Hence if it’s a three digit number, the places will be ones, tens and *hundreds* from right to left. Similarly, for a 4 digit number, it’ll be ones, tens, hundreds and *thousands*. For a five digit number, the leftmost place will be called* ten thousand*. Let’s understand this concept.

Suppose we have a 3 digit number: 345. We can label the places as follows.

Place | Hundreds | Tens | Ones |

Digit | 3 | 4 | 5 |

The value of hundreds place is 100. Similarly, for tens and ones, it is 10 and 1 respectively. As you might remember*,*

*place value= place × digit*

Using the above knowledge, the number **345** can be expanded as= **3×100 + 4×10 + 5×1= 345**.** **Similarly**, **a 5 digit number **54672** is expanded as= **5×10000 + 4×1000 + 6×100 + 7×10 +2×1**

## Large Numbers

Till now we have been studying numbers up to 5 digits. Let us expand our scope to large numbers, starting off with the following knowledge:

- The
*Indian System of Numeration*(i.e. general form of numbers)

Places (left to right in order): Ten crores – Crore – Ten lakhs – Lakhs – Ten thousands – Thousands – Hundreds – Tens – Ones

*The International System of Numeration:*

Places (left to right in order): Hundred million – Ten million – Million – Hundred thousand – Ten thousand – Thousand – Hundred – Tens – Ones

Thus we can expand our understanding of the general form of numbers with 9 digits and more! For example, the expansion of 265478100 is given as= 2×100000000 + 6×10000000 + 5×1000000 + 4×100000 + 7×10000 + 8×1000 + 1×100 + 0×10 + 0×1. Further, its number name is given as:

- Twenty-six crore fifty-four lakh seventy-eight thousand one hundred
*(Indian System)* - Two hundred sixty-five million four hundred seventy-eight thousand one hundred
*(International system)*

## Using Commas

Commas are generally used to ease the process of reading and writing large numbers. For the Indian system of numeration, commas are used to mark thousands, lakhs and crores. On the contrary, for the International system of numeration, commas are used to mark thousands and millions.

Consider the following example: 72705062 can be written as 7,27,05,062 in Indian system whereas it is written as 72,705,062 in the international system.

## Comparing Numbers

With all the information about the general form of numbers, we can easily compare them. When we compare two numbers we start comparing the digits of each number from left. The two scenarios that arise are- they can have an unequal or equal number of digits.

In the first case i.e. for comparing numbers with an unequal number of digits, obviously, the number with more digits is greater. For example- among 12, 123, 1234 and 12345 the greatest number is 12345 since it is a 5 digit number.

For comparison of two numbers having an equal number of digits, we compare the digits at the places starting from left. Example- if we need to compare 4567 and 4578, we start by looking at the digits of both numbers at the leftmost place(here thousand).

As both are the same, we move on to the hundred place. Here also the digit 5 is the same in both. Further, we move on to the tens place. Here we can see that the digit(6) at tens place of 4567 is less than the digit(7) at tens place of 4578. Hence, we conclude that 4578 is greater than 4567.

## Ascending Order and Descending Order

As now know how to compare numbers, we can easily arrange a given set of numbers. We can either arrange the numbers in increasing order *(known as ascending order)*** **or in decreasing order *(known as descending order)***.** Let us understand this with an example:

12, 18, 45, 39, 20, 1, 5

- Ascending order: 1, 5, 12, 18, 20, 39, 45
- Descending order: 45, 39, 20, 18, 12, 5, 1

Note**: **Observe that ascending and descending orders are reverse of each other.

### Solved Examples for You

Ques. Arrange the following in ascending order:

- 847, 9754, 8320, 571

Ans.** **The numbers in ascending order are as follows:

571, 847, 8320, 9754

Ques. What is the ascending order for letters?

Ans. The ascending order basically means the lowest in the order will appear at the top. For the numbers or the amounts. The category is smallest to largest increasingly. Lower numbers or quantities will be at the starting of the list. For the letters, the category is alphabetical and starts from A and goes till Z.

Ques. What does an ascending order mean in Excel?

Ans. The order in which the information is organized or arranged, the ascending order is always organized from the lowest value to the highest value. Such as "1, 2, 3, 4, 5" and "a, b, c, d, e" are both organized in ascending order.

Ques. Is ascending order smallest to largest?

Ans. The numbers are said to be in ascending order when they are organized from the lowest to the biggest number. For example, 5, 9, 11, 13, 17, 19 and 21 are organized in ascending order.

Ques. What is the sign of ascending order?

Ans. For representing this order of numbers we have to use the ascending order symbol i.e. “<“. It signifies numbers from lowermost to uppermost which is opposite to the concept of Descending Order where these numbers are organized from biggest to lowest.

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