# Comparison of Numbers

In comparison of numbers we will learn to compare 4-digit numbers. The same rules are applied to compare numbers having more than 4 digits.

How to learn and understand comparison of numbers?

Rules for Comparison of Numbers:

Rule I: We know that a number with more digits is always greater than the number with less number of digits.

Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits.

To learn and understand comparison of numbers the rules are generalized here:

Rule (1): The number/numeral having more digits is greater.

We know that a number with more digits is always greater than the number with less number of digits.

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

(ii) The number of 3 digits is greater than the number having 2 or 1 digit.

(iii) The number of 4 digits is greater than 3 or 2 or 1 digit number.

(iv) 5-digit number > 4-digit number > 3-digit number ………… etc.

(v) 6-digit number > 5-digit number > 4-digit number ………… etc.

As:

10 > 9;

100 > 99 > 9;

239 > 98;

1250 > 998;

23051 > 8735;

351246 > 92835 > 5298 > 376 > 93.

Example:

Which is greater?

(i) 20,36,15,589 or 6,59,76,456

(ii) 40,201 or 4,999

(iii) 1,29,081 or 90,281

Solution:

(i) 20,36,15,589 or 6,59,76,456

The number 20,36,15,589 has 9-digits and 6,59,76,456 has 8-digits.

So, 20,36,15,589 > 6,59,76,456

(ii) 40,201 or 4,999

40,201 has 5 digits and 4,999 has 4 digits.

So, 40,201 > 4,999

(iii) 1,29,081 or 90,281

1,29,081 has 6 digits and 90,281 has 5 digits.

So, 1,29,081 > 90,281

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

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

In other words;

When the two numbers have the same number of digits, we start comparing the digits from the left most place until we come across unequal digits.

For example:

Compare 29,384 and 20,364

Both numbers are 5-digit numbers.

Let us compare the digits in left most place, we find that both numbers have same digit. Next, we compare the digits in the second most left place, we find that 9> 0.

So, 29,384 > 20,364

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

Follow the below link to understand the examples on comparison of numbers.

A number having the greater number of digits is the greater number.

Example:

Compare 69,56,16,430 and 69,37,82,890

Solution:

Both numbers have same numbers of digits.

Let us compare the digits in the left most place, we find the both numbers have same digits in ten-crores and crores place. Next, we compare the digits at ten-lakhs place. Here 5 > 3.

Thus, 69,56,16,430 > 69,37,82,890.

Solved Examples of Comparison of Numbers:

1. Compare:

(a) 8 and 12.

8 is a single digit number. 12 has two digits.

8 < 12

(b) 1342 and 342

The number of digits in 1342 is greater than the number of digits in 342.

1342 > 342

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

## Ordering of Large Numbers

The numeral with more digits represents the greater number.

For example:

(i) 5,643 > 342

(ii) 11,896 < 121,543

To compare two numbers having the same number of digits we start comparing from the leftmost digit.

How we order the large numbers to compare one number with another number?

3. Compare 19,528 and 25,364

Compare the digits in the ten thousands place.

Since, 1 < 2

19528 < 25364

4. Compare 85,461 and 83,989

Both the numbers have 8 in the ten thousands place.

Therefore, compare the digits in the thousands place.

5 > 3

Therefore, 85,461 > 83,989

5. Compare 6,34,582 and 6,39,285

Both the numbers have 6 in the lakhs place and 3 in the ten thousands place.

So, compare the digits in the thousands place.

4 < 9

Therefore, 6,34,582 < 6,39,285

6. Form the smallest and biggest six digit numbers using the digits 3, 1, 5, 8, 7, 4

Arrange the digits in ascending order.

1, 3, 4, 5, 7, 8

Therefore, the smallest number is 1,34,578.

Arrange the digits in descending order.

8, 7, 5, 4, 3, 1

Therefore, the biggest number is 8,75,431.

Questions and Answers on Comparing and Ordering Numbers:

I. Put the right sign (<, > or =)

(i) 6,397                …………              6,937

(ii) 27,839              …………            25,899

(iii) 32,590              …………            62,890

(iv) 4,15,296           …………          4,27,866

(v) 6,32,700            …………          6,32,200

(vi) 3,20,065            …………         3,20,065

(i) <

(ii) >

(iii) <

(iv) <

(v) >

(vi) =

II. Compare the numbers given below. Put > or < in the box.

(i) 384926             ...........                 348962

(ii) 795642            ...........                 759642

(iii) 562186           ...........                 561286

(iv) 99909             ...........                 99990

(i) >

(ii) >

(iii) >

(iv) <

A. The greatest number among the given is:

(i) 89,306                    (ii) 8,09,306                    (iii) 8,09,606

B. The smallest number among the given is:

(i) 1,28,075                    (ii) 2,18,057                   (iii) 1,39,075

C. I want to buy a car with least price. Which one should I buy?

(i) $5,47,800 (ii)$4,99,900                 (iii) 6,01,800

D. Given below is the population of 3 cities. The most populous city is:

(i) City A - 8,77,310        (ii) City B - 7,92,600       (iii) City C - 5,98,200

E. Given below is the distance of 3 towns from New York. The closest town is

(i) Town A - 8,65,015 m    (ii) Town B - 8,65,880 m   (iii) Town C - 8,70,009 m

A. (iii)

B. (i)

C. (ii)

D. (i)

E. (i)

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