 # Numbers with Digits | Formation of Digits with and without Repetition | How to Form Greatest and Smallest Numbers using Given Digits?

Now, we are going to discuss the Numbers with digits. A group of digits combined together forms the numbers. The digits used for the formation of numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The order of place value of digits starts from right to left i.e. Units, Tens, Hundreds, Thousands, Ten thousand, Lakhs, Ten lakhs, and so on. To solve or to compare any objects first we should form the numbers. Forming numbers can be through with or without the repetition of given digits.

We use numbers not only in mathematics to resolve problems but, also for comparisons in various ways and measuring quantities, and so on. On this page, we learn about the numbers with digits, Solved example problems on Numbers with digits, and so on. This article will surely help you to clear your confusion in every aspect, so without having any delay let’s move ahead and check how to form numbers with digits.

### What are Numbers with Digits?

Numbers with digit means the formation of numbers with the given digits. While forming the numbers first you should know the smallest numbers and greatest numbers. It is done in various ways where we form the digits in our brains. Using digits the formation of the numbers can be done in ascending order or descending order. First, students should clearly know about all types of digits to form the numbers.

We can also know the highest values and lowest values for the forming of numbers with digits. We arrange the given numbers in ascending order, then it is the smallest number. For the greatest number, we arrange the given numbers in descending order.

### Rules for Forming the Numbers with Digits | How to form Numbers with Digits?

Rules to follow for forming the numbers with digits are given in the below section to have an idea of how to form numbers with digits. By, following certain rules, we can easily make the numbers. The rules are,

• To arrange the given digits in ascending order from left to right, the greatest number is formed. In the greatest number, the extreme left digit has the highest value compared to others.
• To arrange the given digits in descending order from left to right, the smallest number is formed. In the smallest number, the extreme left digit has the lowest value compared to others.
• Zero is one of the digits while forming the smallest number, zero is not placed at the extreme left place it is written in the second-highest place or after the highest place. If we want to form the greatest number, the zero is placed at the extreme left place (i. e., highest value).

### Solved Examples on Numbers with Digits

Example 1:
Write the smallest number using the below digits,
3, 0, 4, 6, 5

Solution:
In the given question, the digits are 3, 0, 4, 6, 5
Now, we can write the smallest number using given digits.
So, the number is 30,456
Therefore, using the given digits the smallest number is 30, 456.

Example 2:
Write the smallest number and greatest number using the below digits,
8, 7, 3, 6, 2

Solution:
In the given question, the digits are 8, 7, 3, 6, 2
Now, we can write the smallest number and greatest number using given digits.
Therefore, the smallest number is 23,678,
The greatest number is 87,632
Hence, using the given digits the smallest number is 23,678 and the greatest number is 87,632.

Example 3:
Write the greatest number using the below digits,
9, 5, 2, 1, 4

Solution:
In the given question, the digits are 9, 5, 2, 1, 4
Now, we can write the greatest number using given digits.
So, the number is 95,421
Therefore, using the given digits the greatest number is 95,421.

Example 4:
Explain how to write the greatest and smallest 4 digit numbers using the digits 2, 4, 6, 9

Solution:
In the given question, the digits are 2, 4, 6, 9.
The given four-digit number has four places those are thousands, hundreds, tens, and ones.
If we arrange the given digits are in descending order (from greatest to lowest value), we get the greatest number. If the given digits are arranged in ascending order (from lowest to highest), we get the smallest number.
The descending order is 9< 6< 4 < 2.
The ascending order is 2 < 4 < 6 < 9

Th      H       T       O

Greatest number           9       6       4       2
Lowest Number            2       4        6        9
Therefore, using given digits the greatest number is 9,642 and the smallest number is 2,469.

Example 5:
Write the greatest and smallest two-digit numbers formed with the following given single digits:
(i) 8, 5
(ii) 7, 9
(iii) 2, 6
(iv) 0, 4

Solution:
In the given question, a few single digits are given.
Now, we can form a 2-digit number using given single digits.
The following are,
(i) The given digits are 8 and 5,
Now, using given single digits we can write the greatest and smallest 2-digit numbers.
So, the greatest number is 85 and the smallest 2-digit number is 58.
Therefore, with the given single digits, the formed 2-digit numbers are 85 and 58.

(ii) The given digits are 7 and 9,
Now, using given single digits we can write the greatest and smallest 2-digit numbers.
So, the greatest number is 97 and the smallest 2-digit number is 79.
Therefore, with the given single digits, the formed 2-digit numbers are 97 and 79.

(iii) The given digits are 2 and 6,
Now, using given single digits we can write the greatest and smallest 2-digit numbers.
So, the greatest number is 62 and the smallest 2-digit number is 26.
Therefore, with the given single digits, the formed 2-digit numbers are 62 and 26.

(iv) The given digits are 0 and 4,
Now, using given single digits we can write the greatest and smallest 2-digit numbers.
So, the greatest number is 40 and the smallest 2-digit number is 04.
Therefore, with the given single digits, the formed 2-digit numbers are 40 and 04.

Example 6:
With the help of the given digits, form 3-digit numbers as many as you can. But no digit should be repeated in any of the formed 3-digit numbers.
(i) 2, 4, 9
(ii) 5, 1, 7
(iii) 3, 1, 8

Solution:
In the given question, few single three digits are given to form a 3-digit number but no digit should be repeated.
Now, we can write or form the 3-digit number using given digits.
The following are,
(i) The given single three digits are 2, 4, 9
Now, we need to write the 3-digit number but no digit should be repeated.
The three-digit numbers are  249, 429, 294, 924, 492, 942.

(ii) The given single three digits are 5, 1, 7
Now, we need to write the 3-digit number but no digit should be repeated.
The three-digit numbers are  517, 157, 175, 715, 751, 571.

(iii) The given single three digits are 3, 1, 8
Now, we need to write the 3-digit number but no digit should be repeated.
The three-digit numbers are  318, 138, 183, 813, 831, 381.

Example 7:
Write the greatest 3-digit number and smallest 3-digit number without repeating a digit by taking three digits from the following four-digit numbers:
(i) 5, 2, 7, 9
(ii) 6, 1, 0, 2
(iii) 3, 8, 5, 0

Solution:
The given question consists of few four-digit numbers are given.
We can write the three-digit greatest and smallest numbers using given four-digit numbers.
The following are,
(i) The given four-digit numbers are 5, 2, 7, 9
Now, we need to write the three-digit greatest and smallest number without repeating given four-digit numbers.
So, the greatest 3-digit number is 975 and the smallest 3-digit number is 257.
Therefore, using given 4-digit numbers to form the greatest and smallest 3-digit number without repeating a digit. The numbers are 975 and 257.

(ii) The given four-digit numbers are 6, 1, 4, 2
Now, we need to write the three-digit greatest and smallest number without repeating a digit on given four-digit numbers.
So, the greatest 3-digit number is 642 and the smallest 3-digit number is 124.
Therefore, using given 4-digit numbers to form the greatest and smallest 3-digit number without repeating a digit. The numbers are 642 and 421.

(iii) The given four-digit numbers are 3, 8, 5, 0
Now, we need to write the three-digit greatest and smallest number without repeating a digit on given four-digit numbers.
So, the greatest 3-digit number is 853 and the smallest 3-digit number is 035.
Therefore, using given 4-digit numbers to form the greatest and smallest 3-digit number without repeating a digit. The numbers are 853 and 035.

Example 8:
Write the smallest and greatest four digits number using the given digits 6, 1, 5, 3 such that the number thus formed has 6 at its hundreds place and 3 at its one’s place.

Solution:
In the given question, the digits are 6, 1, 5, 3
Now, we need to write the greatest and smallest 4-digits number with given rules.
First, write the smallest digit number is 1356, and the greatest digit number is 6531.
But, we have certain rules to form the smallest and greatest numbers from the question. It says, the number in hundreds place should be 6 and the number at one’s place should be 3.
We will write the smallest number and the greatest number by applying these rules. So, arrange the remaining numbers in ascending order i.e., 1 and 5, and descending order, i.e., 5 and 1.
Therefore, based on given rules the smallest 4-digit number is 1653 and the greatest 4-digit number is 5613.

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