Mathematics is an interesting subject. Students generally start with understanding the concept of formation of numbers. It is then that they will be able to identify the value of a number. The primary step associated with finding the greatest number is to arrange the given numbers into ascending or descending order. This article will discuss the greatest number in details.

Ascending and Descending Order

Before learning about the greatest numbers, let us understand the ordering of numbers. We can arrange the numbers in ascending or descending order.

Ascending order is a sorting method in which numbers are arranged from the lowest to the highest value. Whereas in descending order, the arrangement is from the highest to the lowest.
The descending order plays a significant role in the formation of the greatest number.

How to Find the Greatest Number?

The arrangement of the numbers from the greatest to the least gives us the greatest number, which means writing the numbers in an ordered list of their values.

In the formation of the greatest number, we know the procedure of arranging the numbers in ascending or descending order. The greatest number is formed by placing the given digits in the descending table. This is because of the digit’s position at the extreme left of a number increases.

Greatest Number and Smallest Number

Do you know, by adding \(1\) to the greatest \(1-\) digit number, we can obtain the smallest \(2-\) digit number, and by adding \(1\) to the greatest \(2-\) digit number, we can obtain the smallest \(3-\) digit number and so on. Let us see how it turns out.

When we add one unit to the greatest \(1-\) digit number, we get the smallest \(2-\) digit number.
\(1+9 = 10\)
So, the smallest \(2-\) digit number is \(10.\)
The two-digit number has ones place and tens place. We will get the greatest two-digit number by placing the greatest one-digit number in both ones and tens place. Hence, the greatest two-digit number is \(99.\)

When we add one unit to the greatest \(2-\) digit number, we get the smallest \(3-\) digit number.
\(1+99 = 100\)
The smallest \(3-\) digit number is \(100.\)
Similar to the way we got the greatest two-digit number, the greatest three-digit number is \(999.\)

When we add one unit to the greatest \(3-\) digit number, we get the smallest \(4-\) digit number.
\(1+999 = 1000\)
The smallest \(4-\) digit number is \(1000,\) and the greatest is \(9999.\)

When we add one unit to the greatest \(4-\) digit number, we get the smallest \(5-\) digit number.
\(1+9999 = 10000\)
The smallest \(5-\) digit number is \(10000\), and the greatest \(5-\) digit number is \(99999.\)

When we add one unit to the greatest \(5-\) digit number, we get the smallest \(6-\) digit number.
\(99,999 + 1 = 1,00,000\)
The smallest \(6-\) digit number is \(1,00,000,\) and the greatest \(6-\) digit number is \(9,99,999,\) and so on.
So we can always find a greater number than the given number. This means there is no end to numbers.

Formation of Greatest Number

In the formation of the greatest number, we know the procedure of arranging the numbers in ascending and descending order. The greatest number is formed by placing the given digits in descending order. This is because the digit’s position at the extreme left of a number increases its place value. So the greatest digit should be placed at the extreme left side of the number to enhance its value.

1. When the Given Digits Include Digit \(0.\)

Put the greatest digit at the extreme left, then arrange the remaining digits in descending order of their values with \(0\) at the end.

For example: Form the greatest \(5-\)digit number using the digits \(2,0,8,5,9.\)
Thus the greatest \(5-\)digit number will be \(98,520.\)

2. When the Given Digits Do Not Include Digit \(0.\)

Let us understand this concept by taking an example. Form the greatest number using the digits \(7,6,9,1.\)

Here we have \(4\) digits that are to be arranged in such a way that we get the greatest number.
So, the greatest number should have the greatest digit in the thousands place that is \(9.\)
Then, the next greatest digit, i.e., \(7,\) should be placed in the hundreds place. Then, the next greatest digit in the tens place, which is \(6,\) and the smallest digit in the one’s place is \(1.\)
So, the greatest number formed is \(9761.\)

Let us take another example for a better understanding of the formation of the greatest number. Form the greatest number using the digits \(6,1,9,2,5,4,6.\)
Arrange the given digits in descending order to form the greatest number. Hence, the greatest number is \(96,65,421.\)

3. When the Repetition of Digits is Allowed

When the repetition of digits is allowed, then while forming the greatest number, always repeat the number with the greater value.
For example: Form the greatest \(8-\) digit number using digits \(9,8,5,2,0,1,6\) (You may repeat one of the digits).
So, in this case, while forming the greatest \(8-\) digit number, we will repeat \(9\) as \(9\) is the largest number given in the list.

Hence, the greatest \(8-\) digit number will be \(9,98,65,210.\)

Let’s take another example.
Form the largest \(5-\) digit number using the digits \(7,3,5,0\) (you may repeat the digits twice).
In this case, while forming the greatest \(5-\) digit number, we will repeat the number \(7\) twice, as \(7\) is the largest number given in the list.

Hence, the greatest \(5-\) digit number will be \(77,530.\)

Up for another tricky example??? Well then, let us roll this example as well.
Form the largest \(8-\)digit number using the digits \(6,5.\) You may repeat the digits.
Among \(6\) and \(5,\) \(6\) is the largest number, and thus, we will repeat the number \(6\) to get the largest \(8-\) digit number.

Therefore, the required number will be \(6,66,66,665.\)

Solved Examples – Greatest Number

Q.1. Form the greatest number with the digits \(2, 3, 5, 0\) and \(8\) without repetition of any digit.
Ans: To form the greatest number, we will place the largest digit in the left end and the smallest digit in the right end and then the rest of the digits in descending order from left to right.
Here, the greatest digit is \(8,\) and the smallest digit is \(0.\)
Hence, the largest number that can be formed with the digits \(2,3,5,0\) and \(8,\) without repetition, is \(85,320.\)

Q.2. Find the greatest \(5-\) digit number with \(8\) in hundred’s place and with all the digits different.
Ans: A \(5-\) digit greatest number with \(8\) in hundred’s place and all the digits different can be \(97865.\)

Q.3. Form the greatest \(9-\) digit number using digits \(3,1,4,0,8,7,5,2\) (You may repeat one of the digits).
Ans: The greatest \(9-\) digit number formed by repeating one of the digits is \(88,75,43,210.\)

Q.4. Form the greatest number using digits \(1,9,0,7,8\) and \(5\) only once.
Ans: To form the greatest number, arrange the given digits in descending order.
Therefore, the required answer is \(9,87,510.\)

Q.5. Form the greatest \(4-\) digit number using any four different digits, with the condition that the digit \(5\) is always at ten’s place.
Ans: To form the greatest \(4-\) digit number using any four different digits with the digit \(5\) at ten’s place is \(9,857.\)

Summary

In this article, we learned about the formation of the greatest number when the digits are given. We also learned the greatest of \(1-\) digit, \(2-\) digit, \(3-\) digit, etc., numbers. We knew the fact that by adding \(1\) to the greatest \(1-\)digit number, we can obtain the smallest \(2-\) digit number, and by adding \(1\) to the greatest \(2-\) digit number, we can obtain the smallest \(3-\) digit number and so on.

We have now mastered forming the greatest number when \(0\) is included and also when \(0\) is not included.

Frequently Asked Questions (FAQs)

Frequently asked questions related to greatest numbers is listed as follows:

Q.1. Explain the greatest number with an example.
Ans: The arrangement of the numbers from the greatest to the least means writing the numbers in an ordered list to their values. The largest number should be written on the left, with the following largest number written to its immediate right. The process continues for all the given numbers, and hence, the smallest of the given numbers should be placed on the right.

Put the greatest digit at the extreme left, then put the remaining digits in descending order of their values with \(0\) at the end. For example: Form the greatest \(6-\) digit number using the digits \(2, 1, 8, 0, 4, 9.\) Thus the greatest \(6-\) digit number will be \(9,84,210.\)

Q.2. What is the \(4-\) digit greatest number?
Ans: To form the greatest \(4-\) digit number, we should have the greatest digit, i.e., \(9,\) in all places.

Q.3. What is the \(7-\) digit greatest number?
Ans: To form the greatest number of \(7-\) digits, we should have the greatest digit, i.e., \(9\), in all places.
Therefore, the required greatest \(7-\) digit number is \(99,99,999\).

Q.4. Write the smallest and the greatest \(3-\) digit number.
Ans: The smallest \(3-\) digit number is \(100\) and the greatest \(3-\) digit number is \(999.\)

Q.5. What is the \(3-\) digit greatest number?
Ans: To form the greatest number of \(3-\) digits, we should have the greatest digit, i.e., \(9,\) in all places.
Therefore, the required greatest \(3-\) digit number is \(999.\)

Q.6. What is the \(9-\) digit greatest number?
Ans: To form the greatest number of \(9-\) digits, we should have the greatest digit, i.e., \(9,\) in all places.
Therefore, the required greatest \(9-\) digit number is \(99,99,99,999.\)

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