Comparing Decimals

Comparing decimals in simple terms can be described as comparing two decimal numbers that have decimal values in them. Comparing decimal numbers is the same as comparing whole numbers, but here you have to deal with numbers with decimal values. This concept is useful in real-life situations where precision matters, as numbers with decimal values are quite important if precision is involved. Let’s consider the below question to understand this better.

Question: John has 10 dollars with him, and he wants to buy a candy that is below 10 dollars. He visits a supermarket and finds his two favorite candies, one costs $10.25 and the other one costs $10. Which candy should he buy?

Solution: Let’s understand that the two candies cost around 10 dollars each. But one is pricier than the other. 

    Candy A = 10

    Candy B = 10.25

Here, the difference is 0.25 dollars. 
Thus, John will buy candy A, as this is more feasible for him. 
This method is known as comparing decimals.

What are Decimals?

Decimals are a way of expressing numbers that are not whole and where precision is involved. Decimals have two parts, the whole number part and fractional part. The point present between the two parts is called the decimal point. For example, 445.76 is a decimal number, where 76 is placed after the decimal point.

This decimal point acts as a separator between the whole number and the fractional part. This part represents values smaller than one, and is counted from left to right. While whole numbers are read from left to right, the fractional part is read from right to left.

How to Compare Decimals? 

In order to compare decimals, we have to identify the types of numbers that we get. You can compare two decimal numbers, a decimal number and a whole number. Then we need to identify which of the two decimal numbers is bigger.
 

While comparing decimals and fractions, we have to first convert the given fraction to a decimal. Then, use the same rule as comparing decimals. For example, let’s consider the below question.

Question: Compare 5/2 and 2.57

Solution:

Step 1: First, we have to convert the number which is in fraction. 

        5/2  2.5

Step 2: Now, we have two numbers 2.5 and 2.57. Both have a different number of decimal places

Step 3: Add zeros to 2.5 to match the number of decimal places, writing 2.5 as 2.50. 

Step 4: Now, compare between these two decimal numbers. When we compare the values of both the numbers at their hundredths place after decimals, 7 is greater than 0. At this step, we understand that 2.57 is greater than 2.50. 

Step 5: Hence, we conclude that 2.57 > 2.50 

We already know how to compare decimal numbers, first starting from the whole number part and then moving to the fractional part. At this point, we need to learn how to compare decimals at the hundredths place. Let’s see how to compare them below:

Example: Compare 8.381 and 8.391 to find the larger number.

Solution: 

Step 1: First, we have to compare the whole number. Both of them are 8, so we will move on to the next place value.

Step 2: Look at the tenths place value after the decimals. In both the numbers, we see that the tenth place value is 3. So, we move again to the next place value, which is hundredths.

Step 3: While comparing the next digit, we see that one number has a value greater than the other. 

That is, 9 > 8

Therefore, no need to go further as the answer is clear.

Step 4: Hence, we can conclude that 8.391 > 8.381
 

While comparing the decimal numbers on a number line, we have to visualize the numbers on a number line and then compare them. For example, if we need to compare between 3.1 and 3.4, we will first mark them on the number line in such a way that both of the numbers are included.

Step 1: First, locate all the numbers that you are going to mark on the number line. 

Step 2: We have got 3.1 and 3.4, which are between the numbers 3 and 4. 

Step 3: Use a scale to mark all the tenths decimal values between the 3 and 4 on the number line. 

Step 4: Mark the tenths between 3 and 4, and then locate the given numbers 3.1 and 3.4 on the number line. 

On this number line, we can see that the number line goes from the left to right, the values increase. The number 3.1 is smaller than the number 3.4. 

Thus, 3.4 > 3.1
 

Ordering decimals means arranging them in ascending or descending order based on their values. This process systematically sorts out which number is bigger, smaller, or whether they are equal. This process also involves arranging the numbers in ascending or descending order. Let’s try and solve the below problem to understand this better.

Question: Compare which among the following numbers is smaller and larger: 0.03, 0.30, 0.13, 0.311, 0.131. 

Solution: 

Step 1: First, we need to arrange the numbers in ascending to descending order. For that let’s draw a table with ones, tenths, hundredths, and thousandths.

Step 2: Now, check the tenths decimal values. 

Here, the tenth place values are 0, 1, 1, 3, 3.

    0 < 1, 1, 3, 3

So, we got the smallest number from the group. That is, 0.03.

Step 3: Next, move to the next biggest number the tenths place values are 1, 1, 3, 3. Which is 1. 

Since there are two numbers with 1, we have to move to the next decimal number to know which one is bigger. 

Here, the hundredths place digits are 3 for both numbers. So, we should move to the next decimal number. 

Then the next place value is thousandths, which are 0 and 1. 

            0 < 1

So we get that 0.13 < 0.131. 

Now, we have got 0.03, 0.13, 0.131.

Step 4: Move to the next highest value among 3, 3.

Both of them are equal, so we have to again check the hundredths place value.

The hundredths place values are 0 and 3. So, 0 < 3.

So we get that 0.30 < 0.311. 

Step 5: Arrange them in ascending order. 

 0.03, 0.13, 0.131, 0.30, 0.311

Step 6: Analyze the smallest number and the largest number in the results. Thus, 

 0.03 is the smaller number  
 0.311 is the larger number 
 

Comparing decimals is a valuable skill used in everyday life. From shopping to sports, understanding decimal values helps us make better decisions and accurate comparisons. Here are some real-life examples where comparing decimals is important. 

• Money Transactions: In money transactions that we do in our everyday life from shops to restaurants, we often pay money in decimals. E.g., $75.60. 

• Fuel Prices and Gold Rates: Generally, fuel prices and gold rates go up and down in decimal values. We compare their prices using these decimals. 

• Grades and Test Scores: While finding the average of test scores, the grading system uses decimal values to point out precision. A student scoring 9.6 GPA is higher than the student scoring 9.5 GPA.

• Weather and Temperature: While checking the weather forecast on our mobile phones, we can see the temperature with precision. For example, 32.5° C, 40.2° F, etc.