Subtracting Decimals

Subtracting decimals means finding the difference between decimal numbers and other numbers. The other number can be a whole number, a decimal number, or a natural number. There are certain rules and steps that need to be kept in mind while subtracting decimals. On this page, we will learn more about subtracting decimals, their rules, along with examples.

Subtracting decimals is similar to the usual subtraction of whole numbers. We just need to place the decimal numbers, one below the other, according to their place values along with the decimal point. In some cases the two given numbers are different. If needed, we change the given decimal fractions to like decimal fractions to make the subtraction easier. Two decimals are called like decimal fractions if they have an equal number of decimal places. For example, 0.23 and 0.65 are like decimals, whereas, 7.5 and 7.58 are unlike decimals. After the decimals are converted to like decimal fractions, by adding the required number of zeros, the two given numbers are subtracted in the same way as we subtract regular numbers.

For example, let us subtract the given numbers:

Example: Subtract: 0.56 - 0.42.

Solution:

Since these are like decimals, we will place them in order and do the regular subtraction.

0.56
-0.42
0.14

There are certain rules and steps which should be remembered while subtracting decimals.

• Change the given decimal fractions to like decimals.
• Write the smaller number below the greater number in such a way that the digits are placed in the corresponding places and the decimal points are placed in the same vertical line.
• Then, subtract the numbers in the same way as in the case of whole numbers.
• After the subtraction, place the decimal point in line with the other decimal points.

Subtracting decimals with regrouping is the same as the regrouping that is done in whole numbers. The following steps explain the way to subtract decimals by regrouping.

• Step 1: After changing the numbers to like decimals, and placing the smaller number below the greater number, ensure that the decimal points are aligned and the digits are placed in the corresponding place value column.
• Step 2: Subtract the digits in each column individually, starting from the right and move to the left.
• Step 3: If the number in the upper row is smaller than the number in the lower row, we borrow 1 from the digit to the left and add 10 to the current digit. This step is known as regrouping.
• Step 4: Since 1 had been borrowed, this number is reduced by 1. Change the number accordingly and continue subtracting.

For example, let us subtract the given numbers.

Example: Subtract 0.84 from 0.93.

Solution:

In the above numbers 0.93 and 0.84, the digit 3 is smaller than 4 in the hundredths column, so we need to borrow 1 from 9 to do the subtraction. We need to decrease 1 from 9 since it has given 1 to the number to its left. So, 9 will become 8, and 3 will become 13. Now we subtract 13 - 4 = 9 and 8 - 8 = 0
Finally, we place a decimal point in the answer to get 0.09

Subtracting Decimals with the Same Number of Decimal Places

Subtracting decimals with the same number of decimal places is simple. We just need to do the simple process of subtraction and then place the decimal points according to the given numbers.

For example, let us subtract 3.67 from 4.98

We can see that the numbers have the same decimal places. So, we will subtract them in a regular way.

4.98
-3.67
1.31

Subtracting Decimals with Different Decimal Places

When the numbers have different number of decimal places, they are termed as unlike decimal fractions. In this case, we count the number of digits after the decimal point in both the numbers and identify the higher one in these. Then, we add the required number of zeros to the smaller decimal number to make it to the same length as the other number. After this, we subtract the decimals numbers.

For example, let us subtract 7.483 from 237.8

We can see that both the numbers have different decimal places. Since 7.483 has 3 digits after the decimal, we will add two zeros to 237.8 to bring it to the same length. This will make it 237.800 after which we will subtract the numbers.

237.800
- 7.483
230.317

Subtracting Decimals Within 1

For subtracting decimals within 1, we follow the same procedure that we do in the case of the other decimal numbers. Decimals within 1 mean that the given numbers are less than 1.

For example, let us subtract 0.56 from 0.98.

We can see that the numbers are within one. So, to solve this we will arrange the numbers in order and do the usual subtraction.

0.98
-0.56
0.42

To subtract decimal numbers from whole numbers we place a decimal point in the whole number according to the number of digits (after the decimal) in the other number. Then, we add the required number of zeros so that both the numbers have an equal length.

For example, let us subtract 0.999 from 6.

Solution: Since there are three digits after the decimal in 0.999, we will place a decimal after 6 and add three zeros after it.

Related Articles

Check out the following topics related to subtracting decimals.

• Subtraction
• Binary Subtraction
• Subtracting Decimals Calculator

How to Subtract Decimals When the Top Number is Smaller?

While subtracting decimals, if a number in the upper row is smaller than the number in the lower row, we borrow 1 from the digit to the left and add 10 to the current digit. This process is also called regrouping or borrowing. After this, we change the number accordingly and continue subtracting. Since 1 is given to the following number, this number is reduced by 1. Let us understand this by subtracting the given numbers.

 3.52
-0.45
 3.07

In this case, if we observe the digits in the hundredths column, we see that 2 is smaller than 5, so we borrow 1 from the preceding column (tenths column) and regroup this number, that is, 2 becomes 12. We subtract 5 from 12 and get 7. Now, since 1 was given from the tenths column, 5 reduces to 4, and 4 - 4 = 0. After this, the subtraction continues in the usual way and the answer that we get after subtraction is 3.07.

What are Some Tips for Subtracting Decimals?

For subtracting decimals, we need to remember a few tips which are helpful.

• Write down the numbers in an order such that the bigger number is placed above the smaller one and the decimal points are aligned.
• Add zeros to the required number so that both the numbers are of the same length.
• Then, subtract the numbers in the same way as in the case of whole numbers and place the decimal point accordingly.

How to Borrow When Subtracting Decimals?

While subtracting decimals, there may be instances when a number in the first row is smaller than the number in the second row. In this case, we borrow 1 from the digit to the left and add 10 to the current digit. This process is also called regrouping or borrowing. For example, if we need to subtract 3.58 from 5.4, we see that in the hundredths column, 0 is less than 8.

 5.40
-3.58
1.82

So, we borrow 1 from the tenths column and regroup the number 0 as 10 + 0 = 10. We subtract 8 from 10 and get 2. Now, since 1 was given from the tenths column, 4 reduces to 3 which again leads to borrowing a number from the ones column. So, 3 becomes 13 and we subtract 5 from 13 to get 8. Moving on to the next column (ones column) crossing the decimals, 5 reduces to 4 and 4 - 3 = 1. This gives the final answer as 1.82.

How to Subtract Decimals From Whole Numbers?

To subtract decimal numbers from whole numbers we place a decimal point in the whole number according to the number of digits (after the decimal) in the other number. Then, we add the required number of zeros so that both the numbers have an equal length. For example, to solve these numbers, 4 - 0.67, we can write it as 4.00 - 0.67. Now we can easily subtract the numbers. (4.00 - 0.67 = 3.33)

What is the Rule for Adding and Subtracting Decimals?

The basic rules for adding and subtracting decimals are as follows:

• Change the given decimal fractions to like decimals.
• Align the numbers in such a way that the digits are placed in the corresponding places according to their place values and the decimal points are placed in the same vertical line.
• Then, subtract the numbers in the same way as in the case of whole numbers and place the decimal point accordingly.

How is Adding Decimals Similar to Subtracting Decimals?

Adding decimals is similar to subtracting decimals because the same rules are used in both the cases. We need to place the decimal numbers one below the other, according to their place values along with the decimal point. First of all, we need to change the given decimal fractions to like decimal fractions to make the addition or subtraction easier. After the decimals are converted to like decimal fractions, by adding the required number of zeros, the two given numbers are added or subtracted in the same way as we solve regular numbers.

Give an Example of Subtracting Decimals.

Subtracting decimals is similar to the subtraction of whole numbers. The only thing to be kept in mind is that the decimal points should be aligned and the given numbers should be of the same length. For example, let us subtract 0.456 from 2. For this, we first need to put a decimal point after 2 and place three zeros after that so that the numbers are of the same length. After this, we align the digits and subtract the numbers in the usual way. (2.000 - 0.456 = 1.544)