 # Comparing Numbers

Comparing numbers is a basic concept that we have learned in our primary classes. When we have two numbers or quantities to compare, then we use three basic symbols, they are:

Let us learn in this article, how to compare two numbers and what sign should be used to compare them.

## Less Than, Greater Than, Equal to

The three comparison symbols are less than (<), greater than (>) and equal to (=).

The “equal to” symbol is used to represent two equal numbers or quantities, such as:

3 = 3 or 10 – 7 = 3

The “greater than” symbol is used to show if a number is greater than the other number. For example,

10 > 3 [10 is greater than 3]

The “less than” symbol is used when a number or a quantity is less than the other. For example,

9 < 11 [9 is less than 11]

### Use of Less than and Greater than

The less than and greater than symbols are used based on two numbers given to compare.

A bigger number greater than a smaller number is represented as:

Bigger Number > Smaller Number

A smaller number less than a greater number is represented as:

Smaller Number < Greater Number

## Rules to Compare Numbers

There are certain rules, based on which it becomes easier to compare numbers. These rules are:

• Numbers with more digits
• Numbers starting with a larger digit

### Rule 1: Number with more digits

When we compare numbers, then check if both the numbers are having the same number of digits or not. If a number has more digits, then it is greater than the other number.

Examples:

• 33 > 3
• 400 > 39
• 5555 > 555
• 10000 > 9999

Thus, from the above examples, we can reach the conclusion that:

• Two-digit numbers are greater than single-digit numbers
• Three-digit numbers are greater than two-digit numbers
• Four-digit numbers are greater than three-digit numbers
• Five-digit numbers are greater than four-digit numbers

And so on.

### Rule 2: Numbers Starting with Greater Digit

This rule is applicable when two numbers are having the same number of digits. In such cases, we need to check the digit at the leftmost place, whichever is greater. Therefore, the number with a greater digit at the leftmost place of the number is greater than the other number.

Examples:

• 323>232 [323 is greater than 232]
• 343<434 [343 is less than 434]

Thus, in the above examples, we can see that, when we compare the two numbers, though the number of digits is the same, one number is greater than/less than the other number.

Condition: As we have discussed, if the left-most digit is greater, then the number is the greater one. But if the left-most digit of both the numbers is the same, then we need to check with the second left-most digit. Thus, in this way, we can find the greater or smaller number.

## Solved Examples

Q.1: Which of the following are greater?

1. 21,36,15,589 or 6,49,76,456
2. 41,201 or 5,999
3. 1,39,081 or 91,281

Solution:

1. Given, 21,36,15,589 and 6,49,76,456 are the two numbers.

Since 21,36,15,589 has 9 digits and 6,49,76,456 has 8 digits, therefore, according to rule 1, the number with more digits is greater than the number with fewer digits.

Hence, 21,36,15,589 > 6,49,76,456

2. Given, 41,201 and 5,999 are the two numbers to compare.

Since 41,201 has 5 digits and 5999 has four digits, therefore, according to rule 1, the number with more digits is greater than the number with fewer digits.

Hence, 41201 > 5999

3. Given, 1,39,081 and 91,281 are the two numbers.

Since 139081 has six digits and 91281 has five digits, therefore, according to rule 1, the number with more digits is greater than the number with fewer digits.

Hence, 139081 > 91281

Q.2: Compare the numbers and check which is greater or less.

1. 298 or 512
2. 6138 or 5978
3. 83,449 or 84,449
4. 367825 or 367543

Solution:

1. Since, both the numbers, 298 and 512 are having three digits, thus we will compare the left-most digit of both the numbers.

2 < 5

Therefore,

298 < 512

Hence, 298 is less than 512.

2. 6138 and 5978, both the numbers have an equal number of digits, therefore, we will compare the left-most digit of both the numbers.

6 > 5

Therefore,

6138 > 5978

Hence, 6138 is greater than 5978.

3. 83,449 and 84,449 both the numbers have an equal number of digits, therefore, we will compare the left-most digit of both the numbers.

But the left-most digit is also the same for both numbers, i.e.,8. So, we need to check the second left-most digit.

3 < 4

Therefore,

83449 < 84449

Hence, 83449 is smaller than 84449.

4. 367825 and 367543 both the numbers have an equal number of digits, therefore, we will compare the left-most digit of both the numbers.

As we can see the first three digits are the same for both the numbers, thus we need to compare the next left-most digit of both numbers.

8 > 5

Therefore,

367825 > 367543

Hence, 367825 is greater than 367543

## Practice Worksheets

Students of primary school such as Class 3 and 4 can practise comparing two numbers with these questions.

1. Find the smallest number.

23, 67, 13, 90, 5, 10

2. Compare the numbers and put the appropriate symbol (=, <, >) between them.

9,397 ▢ 9,937

37,839 ▢ 35,899

42,590 ▢ 42,890

5,15,296 ▢ 5,27,866

7,32,700 ▢ 7,32,200

1,20,065 ▢ 1,20,065

## Frequently Asked Questions on Comparing Numbers

### 1. What are the signs used to compare two numbers?

Answer: In Mathematics, we use three basic signs to compare two numbers, they are:

Equal to (=)

Greater than (>)

Less than (<)

### 2. Which is greater 8 or 12?

Answer: 12 is greater than 8. 12 > 8

### 3. How to compare two numbers?

Answer: The number with more digits is the greater number. If two numbers are having the same number of digits, then compare the left-most digits of both numbers.

### 4. Which is greater 0.01 or 0.05?

Answer: 0.05 is greater than 0.01.

### 5. Compare 1/10 and 0.1.

Solution: 1/10 is equal to 0.1.

1/10 = 0.1