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Comparing and Ordering Numbers
Let us first recall the meaning of comparing before learning about comparing numbers. Comparing is the process in which we observe similar properties of different objects or things. Comparing and ordering are an integral part of our everyday lives. Comparing and ordering numbers is a concept in math where we compare the numbers according to their values and identify the smaller and bigger numbers and then order them in ascending or descending order. We compare numbers in our daily lives, for example, by comparing the number of working hours every day, we get to know when we have worked more. We can compare and order numbers in ascending or descending order.
In this article, we will explore the concept of comparing and ordering numbers, the signs used to compare them and learn about comparing rational and integer numbers. We will also learn to compare and order numbers in ascending and descending order with the help of solved examples for a better understanding of the concept.
What is Comparing Numbers?
Comparing numbers is a method of comparing two or more numbers and identifying if one number is equal, lesser, or greater than the other numbers. We use different symbols to write the comparison between numbers. We compare numbers in our daily lives, for example, comparing daily temperature, prices of everyday use items, height, weight, etc. When comparing natural numbers, the number with more digits is greater than the number with a lesser number of digits.
Comparing Numbers Meaning
Comparing Numbers means identifying a number that is smaller or greater than the rest. We can compare numbers using different methods such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc. In our daily lives, comparing numbers is a common practice as we compare numbers with similar properties to identify one number is equal to, smaller than, or greater than the other numbers.
What is Ordering Numbers?
Ordering Numbers is a method of arranging them in order  either from small to big or big to small. When we arrange numbers in ascending order, we arrange them from small to big, and when we arrange numbers from big to small, it is called descending order.
Steps for Comparing Numbers
To learn how to compare numbers, let us go through the steps below:
 Step 1: Compare the number of digits. More number of digits means greater the number.
 Step 2: If the number of digits is the same then compare the higher place values.
 Step 3: If the digits are the same at the highest place value, compare the digits in the next place value to the right.
 Step 4: Keep comparing digits with the same place value until you find digits that are different. The one with the higher face value is the greater number.
Symbols for Comparing Numbers
For comparing numbers, we use specific symbols to identify the greater, smaller, or equal numbers. There are three such symbols. The table given below shows the meaning of each symbol used for comparing numbers.
Symbol  Meaning  Example 

>  Greater than  5 > 3 
<  Less than  2 < 9 
=  Equal to  4 = 4 
The less than and greater than symbols look like the alphabet 'V' placed horizontally. An easy way to memorize the symbols is, the open side of the symbol faces the greater number always, and the pointed end points towards the smaller number. So, if the greater number comes first, then it is a 'greater than symbol >', and if the smaller number comes first, then it is a 'less than symbol <'.
Comparing and Ordering Numbers
Now that we have learned how to compare numbers, we will now discuss how to order numbers after the comparison. We can arrange the numbers after comparing them in ascending order or descending order. Let us understand the meaning of the two methods of ordering:
 Ascending Order: The arrangement of data from the smallest to the largest value is known as ascending order. For example, 1 < 2 < 3 < 4 < 5.
 Descending Order: The arrangement of data from the largest to the smallest value is known as ascending order. For example, 5 > 4 > 3 > 2 > 1.
Comparing Rational Numbers
When comparing rational numbers, we take the LCM of the denominators of the rational numbers being compared. We convert the given rational numbers into like fractions and then compare their numerators. There are some points to remember before learning how to compare rational numbers:
 All negative rational numbers are less than 0.
 All positive rational numbers are greater than 0.
 All positive rational numbers are greater than all negative rational numbers.
Let us now compare two rational numbers to understand the process. Compare 2/3 and 6/7. First, we find the LCM of the denominators of the two given rational numbers. LCM(3, 7) = 21. Now, convert the rational numbers into like rational numbers.
2/3 = (2 × 7) / (3 × 7) = 14/21
6/7 = (6 × 3) / (7 × 3) = 18/21
Now, compare the rational numbers by comparing the numerators of the two like fractions. Since, 18 > 14, so 18 / 21 > 14 / 21. Therefore, we have 6/7 > 2/3.
Important Notes on Comparing and Ordering Numbers
 Comparing numbers is a method of comparing two or more numbers and identifying if one number is equal, lesser, or greater than the other numbers.
 We can order the numbers in ascending or descending order.
 The symbols used for comparing numbers are <, >, and =.
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Comparing and Ordering Numbers Examples

Example 1: Steffy wants to gift a microwave oven to her mom. She saw two ovens having the same features having a listed price of $250 and $252. Which microwave oven should Steffy buy for a good deal?
Solution: To get the best deal, we need to compare the list prices.
Place Value $250
Face values
Comparison $252
Face values
Hundreds 2 = (equal to) 2 Tens 5 = (equal to) 5 Units 0 < (less than) 2 On comparing we find, 250 is less than 252.
Answer: Hence, Steffy should buy the microwave oven which cost her $250 to get the best deal.

Example 2: Megan purchased some items from a store worth $57 but she has $40 only with her. She decided to return the item with the highest price. Which item should she return?
Item Price Noodles $5 Chocolate $18 Corn Flakes $7 Tea $6 Oil $9 Coffee $12 Total $57 Solution: To find the item with the highest price, arrange the prices in ascending order.
{$5, $6, $7, $9, $12, $18}
Now, $18 is at the last. It means it is valued at the highest price. The price of chocolate is $18, so Megan should return the chocolate.Answer: Hence, Megan would return chocolates to buy the remaining items.

Example 3: Compare numbers in the given list and arrange them in descending order.
{10, 3, 4, 0, 8, 4, 2, 1}
Solution: First, we will segregate the negative, positive numbers and 0. {10, 4, 8, 1}, {3, 4, 2}, and 0.
Now, comparing the negative numbers: 1 > 4 > 8 > 10
Comparing the positive numbers: 4 > 3 > 2
Now arranging all given numbers in descending order, we have
4 > 3 > 2 > 0 > 1 > 4 > 8 > 10
Answer: The list in descending order is written as 4 > 3 > 2 > 0 > 1 > 4 > 8 > 10.
FAQs on Comparing and Ordering Numbers
What is Comparing Numbers in Math?
Comparing numbers is a method of comparing two or more numbers and identifying if one number is equal, lesser, or greater than the other numbers.
What is the Rule for Comparing Numbers?
In comparing natural numbers, the number with more digits is always a greater number than the others, and the number with fewer digits is always the smallest.
Why is Comparing Numbers Important in Real Life?
We compare numbers in our daily lives, for example, comparing daily temperature, prices of everyday use items, height, weight, etc. Hence, it is important to learn to compare numbers.
What is Comparing and Ordering Numbers?
Comparing and ordering numbers is a concept of comparing the numbers first and then ordering them in ascending or descending order.
How Do You Compare Whole Numbers?
We can compare whole numbers using a number line.
What is the Difference Between Comparing and Ordering Numbers?
Comparing numbers is just a process of identifying greater and smaller numbers. Ordering numbers involve comparing them along with arranging them in an ascending or descending order.
How to Do Comparing Numbers?
We can compare numbers using different methods such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc.
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