Comparing Numbers

 A number is a mathematical object used to count, measure, and also label.

What are Natural numbers?

  • Counting numbers 1, 2, 3, 4, ...... etc. are called Natural numbers.
  • The smallest natural number is 1 and there is no largest natural number.

Digits and Place value

  • Numbers are formed using the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These symbols are called digits or figures.
To find the place value of a digit in a number, multiply the digit with the value of the place it occupies.

Comparison of Numbers

We often need to compare the two or more numbers. Here are some of the ways it can be performed easily
1) If two numbers have unequal number of digits,
  • then the number with the greater number of digits is greater.
2) If two numbers have equal number of digits then,
  • the number with greater valued digit on the extreme left is greater.
  •  If the digits on extreme left of the numbers are equal then the digits to the right of the extreme left digits are compared and so on.
Example:

a) Comparison between 358 and 4567
Answer: Here,
4567 has four digits and
358 has three digits,
so clearly 4657 is greater than 358

b) Comparison between 1345 and 2456
Answer:  Here both the number have same digit,
So we need start looking at the extreme left digit
1345 -> 1
2456 -> 2
Now 2 > 1
So we can clearly state 2456 > 1345

c) Comparison between 4345 and 4656
Answer:Here both the number have same digit,
So we need start looking at the extreme left digit
4345 -> 4
4656 -> 4
As they are same, we need start looking at second extreme left digit
4345 -> 3
4656 -> 6
Now 6> 3
So we can clearly state 4656 > 4345

Some Important Terms

  • The arrangements of numbers from the smallest to the greatest is called Ascending order.
  • The arrangement of numbers from the greatest to the smallest is called Descending order.
Example

Q) Arrange the following in ascending order: 5392, 5782, 5789, 5654
Answer:
The above rules of comparison can be applied here also.
Here all the number are of same number of digit and extreme left digit is also same.So we need to look at second extreme left digit

So 5782,5789 > 5654 > 5392

Now in 5782,5789, unit place makes the comparison easier

5789> 5782 > 5654 > 5392

So ascending order would be
5392 < 5654 < 5782 < 5789

Number Formation

Question : Form the largest and the smallest possible numbers using 3,8,1,5 without repetition

Largest number will be formed by arranging the given numbers in descending order – 8531

The smallest number will be formed by arranging the given numbers in ascending order – 1358