Page 22 - ICSE Math 6

• To form the greatest number with the given digits, place the greatest digit at the extreme left
position, and then place the remaining digits in descending order of their values.

Example 7: Form the smallest 3-digit number using the digits 4, 9 and 0 without repetition.
Solution: Place the smallest digit (except 0), i.e., 4 at the extreme left position. Then, place 0 and
then 9. So, the required smallest 3-digit number is 409.

If 0 is used at the extreme left position, then the number formed will be 049, which is a 2-digit
number.

Example 8: Form the smallest and the greatest 6-digit numbers using the digits 8, 9, 1, 0, 4 and 6
without repetition.

Solution: To form the smallest 6-digit number, place the smallest digit (except 0), i.e., 1 at the
extreme left position. Then, place the remaining digits 8, 9, 0, 4 and 6 in ascending
order. So, the required number is 1,04,689.

To form the greatest 6-digit number, place the greatest digit, i.e., 9 at the extreme left
position. Then, place the remaining digits 8, 1, 0, 4 and 6 in descending order. So, the
required number is 9,86,410.
Example 9: Form the smallest and the greatest 6-digit numbers.
Solution: The smallest digit except 0 is 1. So, place 1 at the extreme left position and then five
0s on its right. So, the smallest 6-digit number is 1,00,000.

The greatest digit is 9. So, place 9 at all the six places to get the greatest 6-digit number as
9,99,999.
Example 10: How many 4-digit numbers are there between 999 and 4,000?

Solution: The required 4-digit numbers are from 1,000 to 3,999.
There are 1,000 numbers from 1,001 to 2,000, 1,000 numbers from 2,001 to 3,000 and 999
numbers from 3,001 to 3,999. Since 1,000 also comes between 999 and 4,000, so there are
1,000 + 1,000 + 999 + 1 = 3,000 numbers between 999 and 4,000.

EXERCISE 1.2

1. Form the smallest 3-digit number using the given digits without repetition.

(a) 4, 9, 2 (b) 3, 9, 0 (c) 0, 2, 1 (d) 9, 8, 1
2. Form the greatest 5-digit number using the digits 9, 1, 0, 6 and 2 without repetition.
3. Form the smallest and the greatest 4-digit numbers using the digits 5, 6, 9 and 0.

4. Form the greatest and the smallest 4-digit numbers.
5. Form the smallest 6-digit number with 4 at tens place.
6. Fill in the blanks.

(a) The smallest 5-digit number is __________.
(b) The sum of the largest 4-digit number and the smallest 5-digit number is __________.
(c) In the greatest 6-digit number, the digit at hundreds place is __________.
(d) In the smallest 6-digit number, the digit at tens place is __________.
7. How many 3-digit numbers are there between 99 and 3,000?

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