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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