Subtraction of decimals is finding the difference between two or more decimal numbers and other numbers like whole, decimal, or natural numbers. The subtraction of decimals is similar to the subtraction of whole numbers.
Subtraction of Decimal
To find the subtraction of decimals, take two decimal numbers, one below another, place the decimal point, and adjust the digits according to their place values. Some rules and steps are followed while subtracting decimals.
Subtracting Decimals
Subtracting decimals means finding the difference between two or more decimal numbers.
To subtract decimals using the column method, align the digits with the same place values (ones, tenths, hundredths, etc.). Start by placing the larger decimal number on top and the smaller one below.
If their decimal places are unequal, add zeros to make them equal. Then, subtract, as usual, starting from the rightmost column. If the larger number is on top, find the positive difference. If the smaller number is on top, find the difference and change its sign to negative.
For example, to subtract 0.53 from 0.87, align them as 0.87 - 0.53. If there's a difference in decimal places, add zeros to make them equal, like changing 5.4 to 5.40. Subtract normally to find the result.
Rules for Subtracting Decimals
There are certain rules that should be followed while subtracting the decimals:
- Convert the decimal fractions to decimals.
- Use column subtraction so that the larger number is above the smaller number. Make sure the decimal places of two numbers are on the same line.
- Always subtract the digits from Right to left.
- If the digit is smaller to subtract the other digit in the lower row then borrow from the left number.
- Place the decimal point after subtraction which is as many decimal places similar to the subtracting numbers.
- Check whether the subtraction is between the smaller decimal and larger decimal or between the larger decimal and the smaller decimal.
- If the subtraction is between the smaller decimal and the larger decimal then include a negative sign in the answer.
Example of Subtracting Decimals
For Example, lets consider Subtraction of 4.20 from 5.3
Add 0 after 5.30 to make equal digits in both the decimals,
Thus, we have to simplify 5.30 - 4.20. This can be subtracted as following illustration:
Subtracting Decimals with Regrouping
The steps that are used in subtracting decimals with regrouping:
- Convert the decimal fractions to decimals and place the larger number above the smaller number.
- Check the decimal places of two numbers are on the same line.
- Subtract the digits from right to left.
- Check if the digit is smaller than the other digit in the lower row, borrow 1 from the left digit add that 1 to the smaller digit so 10 is added to smaller digit which is called as Regrouping.
- As 1 is borrowed from left, then 1 is reduced from that number so the number is changed. Continue the subtraction until to reach the left end.
Let's consider an example for better understanding.
Example: Subtract 3.46 from 6.52.
Solution:
In Hundredth place,
As 2< 6, borrow 1 from left digit (5), then add 10 to 2 (10+2=12), Subtract 6 from 12 (12-6=6)
In answer 6 will be in hundredths place.
In tenths place,
As 1 is borrowed to the right digit , so reduce 1 from this digit (5-1 = 4) then Subtract 4 from 4 (4-4).
In answer, 0 will be in tenths place.
In ones place,
Subtract 3 from 6 (6-3).
In answer, 3 will be in ones place.
So, The answer is 6.52- 3.46 = 3.06.
Subtracting Decimals with the Same Number of Decimal Places
Subtracting Decimals with the same number of decimal places means, For Example, Subtraction of two decimals, The two decimals have the same number of decimal places.
Place the larger decimal upon the smaller decimal to find the subtraction.
Example: Subtract 5.32 from 7.52.
Subtracting Decimals with Different Decimal Places
Subtracting decimals that are having same decimal places are simple, but subtracting the decimals with different decimal places requires to add zeros as many as after the decimal point to the decimal that has fewer digits than the other decimal.
Example: Subtract 251.4 from 356.7893.
Solution:
As 356.7893 having 4 digits after decimal point, but 251.4 is having 1 digit after the decimal point, so to make them equal add 3 zeros to 251.4 i.e, 251.4000.
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Subtracting Decimals Within 1
Subtracting decimals within 1 means subtracting the numbers that are less than 1.
Example: Subtract 0.42 from 0.99.
Solution:
To subtract 0.42 from 0.99, write them in the
Subtracting Decimals From Whole Numbers
Subtracting decimals from whole numbers means, For a two-number subtraction one number is decimal and the other is a whole number. Add decimal points and zeros to the whole number as many as the decimal does.
Example: Subtract 0.99 from 8.
Solution:
Add two zeros to 8, since there are two digits after decimal.
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Conclusion
Decimals in mathematics place an important role for dealing with money, weight, length, etc. Subtracting decimals that are with regrouping, with the Same Number of Decimal Places, with Different Decimal Places, From Whole Numbers are used in these real time applications.
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Solved Examples on Subtracting Decimals
Example 1: Subtract 7.2298 from 3.4456.
Solution:
Subtract 7.2298 from 3.4456 means,
3.4456-7.2298
Take the larger decimal (7.2298) above the smaller decimal(3.4456),
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7.2298 - 3.4456 = 3.7842
Place negative sign in answer as ( 3.4456 < 7.2298),
So, 3.4456-7.2298 = -3.7842
Example 2: Subtract 3 from 4.876.
Solution:
Subtract 3 from 4.876 means, 4.876 - 3.
Take the larger decimal (4.876) above the smaller decimal(3),
Add 3 zeros to 3 to make 3 (whole number) to 3.000(decimal),
So, 4.876-3 = 1.876
Example 3: Calculate 2567.90-2394.34.
Solution:
Take the larger decimal ( 2567.90) above the smaller decimal(2394.34),
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So, 2567.90-2394.34 = 173.56
Practice Questions on Subtracting Decimals
Problem 1: Simplify
- 5.78 - 2.94
- 10.6 - 4.27
- 15.82 - 8.95
- 23.46 - 6.73
- 32.17 - 19.83
Problem 2: Subtract 2.21 from 7.
Problem 3: Subtract 3.301 from 5.1234.
Problem 4: Subtract 12 from 11.071.
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