Imagine you want to buy your favourite comics. You visit two shops searching for the comic, one store was selling it for 165/- and the other for 195/- respectively. Well, you obviously buy it from the first store. How did you make this decision? Well, you compared their prices. Let us learn more about comparing numbers.
Let us recollect the number line. Natural or whole numbers on a number line increase from left to right. It starts from zero and increases all the way to infinity. So when we compare any two numbers, the number on the right will always be greater than the one on the left,
For example, from the numbers 11, 34, 98 which is the greatest? Well, the answer is 98 of course. And if you imagine these numbers represented on the number line, you will notice that 98 is the number most on the right. 11 and 34 were to the left of 98, making it the greatest number.
Representation of the Comparison
Let us now focus on how we represent this comparison of numbers. There are some special mathematical signs involved.
|>||Indicates Greater Than|
|<||Indicates Lower Than|
|=||Indicates equal to|
Let us understand this with a few examples. For the first one, you will be comparing two numbers, 7 and 65. Here it is abundantly clear that 65 is the greater number. Which means 7 is the smaller number. It can be said that 7 is lower than or less than 65. So this comparison can be written as 7 < 65.
Similarly, we can also say that 65 is bigger than or greater than 7. And this comparison will be expressed as 65 > 7. While both of these mean the same thing, the way we express it may differ.
Comparison of Larger Numbers
Now it easier to compare smaller numbers. Comparing one, two even three digit numbers. But when the numbers get bigger, the task gets a little harder. Especially if the numbers you are comparing are not all of the same numbers of digits. So we always start by finding if the numbers have the same number of digits. Otherwise, the number with the higher number of digits is obviously the bigger number.
Example: Compare the numbers 4532, 4567, 8766 and 12345.
- Over here as you can see the last number has 5 digits while the others have four. So that is the biggest number followed by the rest.
- Amongst the rest, the ones right on the number line are bigger. We compare the first digit and pick 8766 as the bigger number.
- Then the two remaining numbers both start at 4.
- So we move to the second digit and find that they are also the same.
- Then when we see the third digit we will notice that 6 is greater than 3 and hence 4567 is greater than 4532.
- Finally we arrive at the result, which is 12345> 8766 > 4567 > 4532
Solved Examples for You
Question 1: Compare and put the appropriate sign:
100002 ___ 1000002.
- None of the above
Answer : The correct answer is “A”. Number 1000002 is a seven digit number, while 100002 is a six-digit number. Hence 100002 < 1000002
Question 2: Why we compare numbers?
Answer: We compare numbers because it is useful when we are dividing because if the number you are dividing by is larger than you know that you will get a decimal for your answer. Furthermore, we have symbols to note when one larger number is larger than, smaller than or equal to another.
Question 3: Which place value is best suited for comparing the numbers?
Answer: While comparing numbers, first of all, start with the greatest place value. After that, compare the digits in the greatest place value position. Also, if these digits are the same, then continue to the next smaller place until the digits are different.
Question 4: How to compare two numbers as a percentage?
Answer: For comparing two numbers as a percentage firstly, figure out the difference between them. Thereafter, divide the increase new number by the original number and multiply the answer by 100.
Question 5: What number is a composite number?
Answer: These are positive integers that are not prime (that is numbers that have factors other than 1 and itself). In addition, we can summarize the first few composite numbers which we sometimes refer to as short are: 4, 6, 8, 9, 10, 12, 14, 15, 16, etc.