Comparisons



To study and recognize comparison of numbers the rules are generalized here:
Rule (1): The number/numeral having more digits is bigger

(i) The 2 digits  number  is bigger than the one digit number.

(ii) The 3 digits  number is bigger than the 2 or 1 digit number.
(iii) The4 digits number is bigger than 3 or 2 or 1 digit number.

(iv) 5-digit number is bigger than  4-digit, 3-digit ,2 digit and 1 digit number.

(v) 6-digit number is bigger than  5-digit number > 4-digit , 3-digit ,2 digit and 1 digit number.

As:

12 > 6, 120 > 15 > 4, 458 > 86, 1550 > 789, 25065 > 6543, 654613 > 82354 > 4350 > 540 > 75.

Rule (2): (a) If two numbers have the same number of digits, we evaluate them on the base of their extreme left digits. The number with the bigger extreme left digit is bigger.

As:

(i) 514 > 298, because 5 > 2

(ii) 6138 > 5978, because 6 > 5

(iii) 32516 > 19768, because 3 > 1

(iv) 451926 > 351658, because 4 > 3

(b) If the extreme left digits of two numbers are the same, we compare them on the basis of the next digits towards their right and so on.

As:

(i) 64283 > 63198, because 6 = 6, but 4 > 3

(ii) 24567 > 22381, because 2 = 2, but 4 > 2

(iii) 83,643 > 83,449, because 83 = 83, but 6 > 4

(iv) 367825 > 367543, because 367 = 367, but 8 > 5

These are the rules to teach comparison of numbers. Parents and teachers can also try these rules to guide the students how to compare numbers.

A number having the greater number of digits is the greater number.
Examples of Comparison of Numbers
1. Compare: 
(a) 9 and 15.

8 is a single digit number. 12 has two digits.
9 < 15

(b) 2345 and 123

The number of digits in 1342 is bigger than the number of digits in 342.
2345> 123
If two numbers have the same number of digits, then line up the digits according to place value. Compare the digits beginning with the greatest place. 
2. Compare:

(a) 5869 and 4369
5 > 4
So, 5869 > 4369

(b) 74186 and 74586
7 = 7
4 = 4
1 < 5

So, 74586 > 74186



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