Page 11 - Maths Class 06

The predecessor of a given number is the number that just precedes it, i e. ., ‘the number just before’ the
given number. It is obtained by subtracting one (1) from the given number.

For example, The predecessor of 7,257 is 7,257 – 1 = 7,256
The predecessor of 1,00,000 is 1,00,000 – 1 = 99,999

Formation of the Smallest and Greatest Numbers

Greatest Numbers

To make the greatest number, arrange the given digits in descending order.
For example, The greatest number using the digits 4, 5, 7, 0, 3 only once is 75,430.

Smallest Numbers
To make the smallest number, arrange the given digits in ascending order.
For example, The smallest number using the digits 4, 5, 7, 0, 3 only once is 30457. We do not write 03457
because 0 at the starting of a number has no meaning and the actual value of 03457 is 3457.

EXAMPLE 13. Make the greatest and the smallest 4-digit numbers without repetition of digits such that:
(a) 2 is at tens place (b) 7 is at hundreds place.
Th H T O
SOLUTION : (a) 2 at tens place

Greatest number 9 8 2 7
Smallest number 1 0 2 3
(b) 7 at hundreds place

Greatest number 9 7 8 6
Smallest number 1 7 0 2

Comparing Numbers
We can compare two numbers by the given two rules.
Rule I. A number having more digits will be greater of the two.

e g. ., if we compare 415 and 48, then 415 is greater than 48 because 415 has three digits whereas
48 has two digits.
Rule II. We can compare two numbers having same number of digits by comparing their digits on
extreme left. If the extreme left digits are same, then we compare the next digit to the right of it
and so on.
e g. ., 412567 > 314589, 215823 > 214256, 625089 > 614089.

EXAMPLE 14. By instantly looking at the numbers find which one is the greatest and which one is the
smallest in each of the following?
(a) 23, 567, 198, 79684 (b) 7253, 86, 753, 941
(c) 751534, 963, 7045, 81245
SOLUTION : (a) 23 is the smallest as it contains only 2-digits.
79684 is the greatest as it contains 5-digits which is maximum number of digits
amongst all.

11