Number Comparison, Ordering and Pattern

What are the steps to follow when comparing two numbers?

Step 1:

If the two numbers have different number of digits then the one that has got more digits is greater than the one that has got fewer digits. If they have the same number of digits then go to step 2.

Example:

Number 1: 5647390 (7 digits)
Number 2: 873974 (6 digits)

Number 1 has 7 digits while number 2 has 6 digits. This means that in number 1, the digit in the highest place is in the millions place while in number 2, the digit in the highest place is in the hundred thousands place. Therefore, number 1 is greater than number 2, or number 2 is smaller than number 1. So,

     5647390 is greater than or (more than) 873974 (5647390 > 873974), or

     873974 is less than 5647390 (873974 < 5647390)

Step 2:

If the two numbers have an equal number of digits then you compare the two numbers digit by digit starting from the digit in the highest place value.

Example:

Number 1: 7854912
Number 2: 7832109

The digit in the highest place for both the numbers is 7, which means both numbers start with 7 million, so you can't compare them at this point. So, move on to the second highest digit.

The digit in the second highest place for both the numbers is 8, which means both numbers have 8 hundred thousand, so you can't compare them at this point either. So, move on to the third highest digit.

In number 1, this is 5 while in number 2 it is 3. Clearly 5 is greater than 3, which means number 1 has fifty thousand while number 2 has only thirty thousand. The values of the rest of the digits don't matter and we can conclude that number 1 is greater than number 2 based on the values of the digits in the ten thousands place for the two numbers. So,

     7854912 is greater than (or more than) 7832109 (7854912 > 7832109), or

     7832109 is less than 7854912 (7832109 < 7854912)


How do you arrange two or more numbers in an increasing (ascending) or decreasing (descending) order?

Example:

Number 1: 653981
Number 2: 674190
Number 3: 523716
Number 4: 23989

Use the same steps as in the question above.

First, count the number of digits.

Number 4 has only 5 digits while the rest of the numbers have 6 digits, so number 4 is the smallest of the four numbers.

Now compare the remaining three numbers. The digit in the highest place for number 1 and number 2 is 6, while for number 3 is 5; so number 3 is the second smallest number.

The digit in the next highest place for number 1 is 5 while for number 2 it is 7. So, the third smallest number is number 1 and the biggest of the four numbers is number 2.

After comparing the numbers, they can be either arranged in the increasing or ascending order which means the smallest number to the biggest number, or they can be arranged in the decreasing or descending order which means the biggest number to the smallest number. Here are the two ways of arranging the four numbers above.

Increasing order (ascending order):

     23989, 523716, 653981, 674190


Decreasing order (descending order):

     674190, 653981, 523716, 23989


What are the missing numbers A, B and C below?

A , 5700301, 5800401, B, C, 6100701

To find the missing numbers, first, you need to identify the pattern in the given series of numbers. The given series of numbers is arranged in an increasing order, so let's try to subtract the first given number from the second given number.

     5800401 – 5700301 = 100100

So, the pattern seems to be - going from left to right the numbers increase by 100100. To find the missing number B, add 100100 to 5800401.

     B = 5800401 + 100100
        = 5900501

To find the missing number C, add 100100 to B, i.e. 5900501.

     C = 5900501 + 100100
        = 6000601

To check if we got the pattern right, add 100100 to C and make sure that it is equal to 6100701.

     600601 + 100100 = 6100701

Yes, we got the pattern right!

Finally, to find A, we must subtract 100100 from the first given number as A falls to the left of the first given number.

     A = 5700301 - 100100
        = 5600201

The series with all the missing numbers are filled in is: