Comparison of Two Numbers
If there are two or more things, and we find out the similarities and differences between them which means we are comparing them. By comparison of numbers, we find the numbers are greater than, less than, or equal to other numbers.
Let two friends Sam and Rob stand together. Let us compare their heights.
Whose height is more…?
We can see Sam is taller than Rob. But, how do we got our answer?
We see that they are standing on the same base and Sam’s head is above Rob’s head.
Similarly, we can compare numbers. We can compare the numbers and say whose value is more. We can compare any two numbers and say whether a number is equal to or greater or smaller than the other number.
Symbols Used for Comparison of Numbers
There are three symbols to compare numbers.
‘>’ is a symbol of greater than. It is used when a number is greater than another number. for example, if we compare two numbers 9 and 4 then, we can write
9 > 4
‘<’ is a symbol of less than. It is used when a number is less than another number. for example, if we compare two numbers 2 and 4 then, we can write
2 < 4
‘=’ is a symbol of equal to. It is used when a number is equal to another number. for example, if we compare two numbers 5 and 5 then, we can write
5 = 5
How to Compare Two Numbers?
Case 1: Unequal number of digits in numbers
If the number of digits are unequal in two numbers then the number of more digits is greater.
For example, If we compare 269 and 1652,
1,652 has more digits. so it is greater than 269.
Case 2: Equal number of digits in numbers
Step 1: If the number of digits in two numbers are equal then first, compare the left most digits in the place value representation of the two numbers.
Step 2: If the leftmost digits are the same then move to the second leftmost digit and compare.
Step 3: Continue the process up to which you see an unequal digit.
For example,
Compare 6,528 and 6,594.
Solution:
Both numbers are 4 digit numbers.
Make a place value chart,
Start at the left. Compare the digits in each place until the digits differ,
Compare the thousands,
6,528
6,594 we can see, 6 thousands = 6 thousands
Compare the hundreds,
6,528
6,594 We can see, 5 hundreds = 5 hundreds
Compare the tens,
6,528
6,594 We can see, 2 tens < 9 tens
Therefore we use tens digit to compare the numbers.
So, 6,528 < 6,594
Solved Examples
Example 1: Compare 25,490 and 25,671.
Solution:
Both numbers are 5 digit numbers.
Make a place value chart,
Start at the left. Compare the digits in each place until the digits differ,
Compare the ten thousands,
25,490
25,671 We can see, 2 ten thousands = 2 ten thousands
Compare the thousands,
25,490
25,671 We can see, 5 thousands = 5 thousands
Compare the hundreds,
25,490
25,671 We can see, 4 hundreds < 6 hundreds
Therefore we use hundreds digit to compare the numbers.
So, 25,490 < 25,671
Example 2: Compare 6709 and 569.
Solution:
6,709 is a four-digit number and 569 is a 3-digit number. So,
6,709 > 569
Example 3: Compare 29,650 and 20000 + 9000 + 600 + 60 + 9.
Solution:
Change the numbers to the standard form,
First number is, 29,650
Second number is, 20000 + 9000 + 600 + 60 + 9
Second number is standard form: 29669
Both the numbers are 5 digit number.
Make a place value chart,
Start at the left. Compare the digits in each place until the digits are different,
Compare the left-most digits, i.e. the digits at the ten thousands place,
29,650
29,669
We can see, that the digits are 2 for the the numbers
2 ten thousands = 2 ten thousands
Compare the second left most digit, i.e. the digit at the thousands place,
29,650
29,669
We can see, that the digits are 9 for the numbers
9 thousands = 9 thousands
Compare the third left most digit, i.e. the digit at the hundreds place,
29,650
29,669
We can see, that the digits are 6 for the numbers
6 hundreds = 6 hundreds
Compare the fourth left most digit, i.e. the digit at the tens place,
29,650
29,669
We can see, that the digits are 5 and 6,
5 tens < 6 tens
So, 29,650 < 239,669
Example 4: Put the appropriate symbol <, > or =.
500,225 Five hundred thousand, two hundred twenty-five
Solution:
Change numbers into standard form,
First number is in standard form: 500,225
Second number is Five hundred thousand, two hundred twenty-five.
Standard form: 500,225
Now, we can see that all the digits of both numbers are the same. This gives the result that both the numbers are equal.
500,225 = Five hundred thousand, two hundred twenty-five
Example 5: Two different toy cars cost $1500 and $1551. Which is the lesser price?
Solution:
Price of the first toy car is $1500.
Price of the first toy car is $1551.
Both the numbers are 4 digit numbers.
Make a place value chart,
Start at the left. Compare the digits in each place until the digits differ,
Compare the thousands,
1,500
1,551 we can see, 1 thousand = 1 thousand
Compare the hundreds,
1,500
1,551 We can see, 5 hundreds = 5 hundreds
Compare the tens,
1,500
1,551 We can see, 0 tens < 5 tens
So, we use tens digit to compare the numbers.
$1,500 < $1,551
Therefore, the price of the first toy car is lesser.
No, if a number start with ‘0’ we cannot count this ‘0’ in the number. For example, 0,564 is counted as a three digit number.
No, we first compare the leftmost digits. The number having the greater leftmost digit will be the greater number irrespective of the other digits. For example, if we compare 5,000 and 3,999
The place values of the leftmost digits are 5 and 3. So, compare the leftmost digit i.e. the digit at the thousands place,
5 thousands > 3 thousands
Therefore, 5,000 > 3,999
So, If a number has all the digits greater than another number’s digit except the leftmost digit, it is smaller than the other number.
If the first number is greater than second and second is greater than third. Then the first number will be greater than the third number.
For example, 900 is greater than 500. 500 is greater than 300 then,
900 is greater than 300 also.
900 > 500 > 300