Introduction
Creating the smallest and greatest numbers from a given set of digits is a fundamental skill in mathematics that helps students understand place value and number magnitude.
Explanation Step by Step
To form numbers, we arrange digits according to their values. Here is a reference table for standard smallest and greatest numbers:
| Number of Digits | Smallest Number | Greatest Number |
|---|---|---|
| 1-Digit | 1 | 9 |
| 2-Digit | 10 | 99 |
| 3-Digit | 100 | 999 |
| 4-Digit | 1000 | 9999 |
| 5-Digit | 10000 | 99999 |
Sub-topics
Making the smallest and greatest numbers from given digits
Follow these rules to form numbers efficiently:
- Smallest Number: Arrange digits in ascending order. If there is a 0, place it in the second position from the left.
- Greatest Number: Arrange digits in descending order.
Examples
Example 1: Using digits 9, 2, 6, 4 (once each)
Example 2: Using digits 4, 2, 3 to make a 5-digit smallest number
Tricks and Shortcuts
If you add 1 to the greatest number of n-digits, you get the smallest number of (n+1)-digits. Example: 99 + 1 = 100.
Common Mistakes
Never start a number with 0. For example, using digits 5, 0, 9 to make a 3-digit number as 059 is incorrect; it should be 509.
Practice Questions
Easy Questions
- Form the smallest 3-digit number using digits 5, 2, and 8.
- What is the greatest 4-digit number?
- Using digits 1, 6, 4, form the greatest possible number.
Medium Questions
- Form the smallest 4-digit number using digits 9, 0, 5, 4.
- Using digits 7, 5, 0, form a 4-digit smallest number by repeating digits.
- Arrange digits 3, 6, 2 to form a 5-digit greatest number.
Hard Questions
- What number do you get if you add 1 to the greatest 5-digit number?
- Find the difference between the greatest 4-digit number and the smallest 4-digit number.
- Create the smallest 5-digit number using digits 0, 1, and 2 (you can repeat digits).
Revision Summary
Ascending order creates the smallest number; descending order creates the greatest. Adding 1 to a "all-nines" number transitions to the next place value level.