We will learn forming 2-digit numbers.
How many 2-digit numbers can be formed using the digits 2 and 7?
There are two ways to make 2-digit numbers using the given digits.
I. By repeating the digits - 22 and 77
II. Without repeating the digits - 27 and 72
Thus, there are four 2-digit numbers that can be made using the digits 2 and 7.
Forming Greatest 2-Digit Number:
For Example:
1. Build the greatest 2-digit number possible using the digits 5 and 1.
Step 1: Start with the greatest digit in the greatest place. Since, 5 > 1, put 5 in the tens place.
Step 2: Now put the next greatest digit in the ones place.
If repetition is allowed, the greatest 2-digit number is 55.
If repetition is not allowed, the greatest 2-digit number is 51.
Since 55 > 51, the greatest 2-digit number possible using the given digits is 55.
2. Build the greatest 2-digit number possible using the digits 8 and 4.
Step 1: Start with the greatest digit in the greatest place. Since, 8 > 4, put 8 in the tens place.
Step 2: Now put the next greatest digit in the ones place.
If repetition is allowed, the greatest 2-digit number is 88.
If repetition is not allowed, the greatest 2-digit number is 84.
Since 88 > 84, the greatest 2-digit number possible using the given digits is 88.
Forming smallest 2-digit number
For Example:
1. Build the smallest 2-digit number possible using the digits 2 and 1.
Step 1: Start with the smallest digit in the greatest place. Since, 1 < 2, put 1 in the tens place.
Step 2: If repetition is allowed, the smallest 2-digit number is 11.
If repetition is not allowed, the smallest 2-digit number is 12.
Since 11 < 12, the smallest 2-digit number possible using the given digits is 11.
2. Build the smallest 2-digit number possible using the digits 7 and 3.
Step 1: Start with the smallest digit in the greatest place. Since, 3 < 7, put 3 in the tens place.
Step 2: If repetition is allowed, the smallest 2-digit number is 33.
If repetition is not allowed, the smallest 2-digit number is 37.
Since 33 < 37, the smallest 2-digit number possible using the given digits is 33.
3. Build the smallest 2-digit number possible using the digits 6 and 0, without repeating any of the digits.
0 < 6, but starting with zero makes 06, which is not a 2-digit number.
Hence, we begin with the next smallest digit which is 6.
Now put the next smallest digit which is 0 in the ones place. Thus, 60 is the smallest 2-digit number formed using the given digits.
Questions on Forming 2-Digit Numbers:
I. Write the greatest and smallest 2-digit numbers formed by the following digits, given that the repetition of digits is allowed.
(i) 1, 9 __________; __________
(ii) 0, 7 __________; __________
II. Build the numbers using the given digits in each of the following, without repeating any of the digits.
(i) The greatest 2-digit number using the digits 5 and 7
(ii) The smallest 2-digit number using the digits 0 and 8
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