Subtracting Decimals

Subtracting decimals is similar to regular subtraction, but the key difference is that you need to carefully handle the decimal digits. Subtracting decimals means finding the difference between two decimal numbers or decimal number and a whole number. 

There are two types of decimal numbers, like decimals and unlike decimals. Like decimals have the same number of decimal places, while unlike decimals have different numbers of decimal places. 

For example, 2.24 and 3.75 both have two decimal places (0.24 and 0.75). Another example, 5.676 has three decimal places, while 1.90 has two, making them unlike decimals.
 

In order to subtract decimals, you need to follow the correct order of place values of the numbers along with their decimals. That is, 

Step 1: Identify the whole number and decimal parts of each number. For example, in 22.04 and 33.567, the whole numbers are 22 and 33, and the decimal parts are 0.04 and 0.567.

Step 2: Now, consider the decimal part, where the number 22.04 has two decimal places and number 33.567 has three decimal places. Align decimal points vertically to match corresponding place values (tenths, hundredths, etc.).
            
                     
Step 3: Subtract the two decimal numbers. 

    Start from the rightmost digit (thousandths place): 7 – 0 = 7

    Move to the next place (hundredths place): 6 – 4 = 2, subtract 4 from 6.

    Move to the tenths place: 5 – 0 = 5

Now, subtract the whole numbers:

 3 – 2 = 1

 3 – 2 = 1

Step 4: So, the answer you get is 11.527.
 

Once you understand the process, follow these rules to subtract decimal numbers: First, align the numbers vertically by their decimal points, ensuring that whole number digits (ones, tens) and decimal digits (tenths, hundredths) correspond.
Let’s quickly take a look at the rules that we must follow.

• When two numbers are given, check the numbers first. If it’s a fraction, convert the fraction into decimals.

• Then place the numbers in such a way that the whole number digits should be placed corresponding to their place values (ones to tens), and the decimals should be placed in a vertical line, from the left to right should be tenths, hundredths, thousandths …

• Subtract the subtrahend (second number) from the minuend (first number). If the result is negative, include the negative sign.

• Then, subtract both the whole number and the decimal digits, starting from the right side.
   

Subtracting decimals with regrouping means subtracting the two numbers just like how you subtract between whole numbers. Let’s look at them step-by-step.

Step 1: Let’s take an example of 7.3 and 2.45. First, we have to convert the numbers into decimals. 

Convert 7.3 into two decimal places  7.30. 

Step 2: Next, regroup the numbers, that is, subtracting the smaller number from the larger number (if not specified).

Step 3: Subtract the hundredths place of the decimal first. 

Since 0 is smaller than 5, we will borrow 1 from the tenths place (3 of the top number).

    The 3 becomes 2, and we add 10 to the hundredths place. 

    So, 10 – 5 = 5. 

    Hundredths place in the answer: 5

Step 4: Next subtract the tenths place.

After borrowing, the digit in the tenth place is 2 (top) and 4 (bottom).

Since 2 is smaller than 4, we borrow 1 from the one's place (7) of the whole number part.

The 7 becomes 6, and we add 10 to the tenths place.

10 + 2 = 12

Now subtract 12 – 4 = 8

Tenths place in the answer: 8

Step 5: Subtract the ones place of the whole number.

6 – 2 = 4

    Ones place in the answer: 4

Step 6: So the answer you get is 4.85.
 

Subtracting decimals from whole numbers means that you have to subtract one decimal number from another number (which is a whole number). For this, you have to first make the whole number as like decimals by adding zeros after the decimal point. For example, 

Question: Subtract 3.33 from 10.

Solution: First, add two zeros to the number 10. 

Then, start the subtraction process.  

Here, in the hundredths place, the top number is 0 (zero). So we have to borrow from the tenths place. 

But the tenths place is also a zero, so we borrow from the next decimal place, which is ones of the whole number parts. 

In the ones place of the whole number part, it is again a zero (0). So we move to the next place value, which is tenths. From one (1) we borrow. 

After borrowing from one place, the tenths place becomes 10, and after borrowing from the tenths place, the hundredth place becomes 10.

Now, subtract accordingly 

    
Answer: So the answer is 6.67.
 

This refers to subtracting two decimals numbers, both less than 1. For example, 

Question: Subtract 0.03 from 0.85.

Solution: First, analyze which decimal value is greater. Then subtract the smaller one from that. 

    
 
Then subtract it, following the same steps we did in the previous sections. 

Answer: The answer you get is 0.82.
 

Subtracting decimals with the same number of decimal places is like basic subtraction. In the subtraction, it is advisable to ignore the decimal point. For example, 

Subtract 6.88 from 8.12.

Solution: You can directly start subtracting, since there are an equal number of decimal places. 

Answer: The answer you get is 1.24.
 

While subtracting numbers with different decimal places, it is always mandatory to align the numbers by adding zeros. For example, 

Subtract 2.51 from 45.678.

Solution: Add zeros to the number with fewer decimal places to match the other.

Then subtract the values following the steps we did in the previous sections.

Answer: The answer you get is 43.168.
 

Subtracting decimals is a useful skill in everyday life, from handling money to weight differences. Here are some real-life examples where subtracting decimals helps solve common problems. 

• Money Transactions: Subtracting decimals is essential for money transactions, such as calculating change or comparing prices.

• Measuring Ingredients While Cooking: Recipes often require precise measurements, and subtracting decimals helps you determine the remaining amount of an ingredient. For example, if you have 2.5 cups of flour and need 1.75 cups, subtracting decimals (2.5 – 1.75 = 0.75) tells you how much flour remains.

• Height Differences: Subtracting decimals helps determine height differences between people, buildings, or plants. 

• Weight Difference: Subtracting decimals is useful when comparing the weights of objects, such as fruits, packages, or even people.