Adding and Subtracting Decimals

Addition And Subtraction Of Decimal

Edited By Team Careers360 | Updated on Jul 02, 2025 05:17 PM IST

Decimal addition and subtraction are slightly more complicated than natural number operations. In order to learn addition and subtraction of decimal numbers, first we have to understand the decimal numbers. When we have to present any number with high precision, we use decimals. Decimal numbers are presented by using points in between the numbers. All fraction numbers can be written in decimal form.

This Story also Contains

Decimal Addition And Subtraction
Steps In Addition Of Decimal
Example Of Addition
Steps In Subtraction Of Decimal
Example Of Subtraction
Frequently Asked Questions

Let us take an example of decimal: suppose you have 100 rupees and you have to divide it among 11 members. Now here rupees received by each person will not be an integer. Here each person will receive rupees between 9 to 10. So in this type of problem, we used addition, division, multiplication and subtraction on decimal numbers. So understanding mathematical operations on decimal numbers is very important for us.

Decimal Addition And Subtraction

In mathematics addition, subtraction and other mathematical operations are easily applicable to natural numbers. If we talk about mathematical operations on decimal numbers it is not the same as in natural numbers. We have to follow some steps for applying mathematical operations in decimal numbers.

Steps In Addition Of Decimal

Following steps should be followed for the addition of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start adding each corresponding digit and addition should start from the right side.
After addition make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

Example Of Addition

Suppose in your class the teacher asked you to add the marks of two of your friends. One friend got 75.25 marks and the other friends got 85.5 marks.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. Here in this question, one number has 2 digits after the decimal and one number has one digit after the decimal so to make them similar place zero at the right of the 5 in 85.5.

Now 85.5=85.50

Add 75.25 and 85.50

\[75.25 + 85.50 = 160.75\]

Steps In Subtraction Of Decimal

Following steps should be followed for the subtraction of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start subtracting each corresponding digit and subtraction should start from the right side.
After subtraction make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

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Example Of Subtraction

Suppose in your class the teacher asked you to subtract the marks of two of your friends. One friend got 75.25 marks and the other friends got 85.5 marks. The teacher asked to subtract 75.25 from 85.5

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. Here in this question, one number has 2 digits after the decimal and one number has one digit after the decimal so in order to make them similar place zero at the right of the 5 in 85.5.

Now 85.5=85.50

Subtract 75.25 from 85.50

\[85.50 - 75.25 = 10.25\]

Frequently Asked Questions

Explain Decimal Numbers.

Ans. It is a number which is a combination of whole numbers and fractional numbers. Decimal numbers are presented by using points in between the numbers.

Explain the addition.

Ans. The process of joining two small numbers in mathematics and creating one larger number is known as an addition.

Explain the Subtraction.

Ans. Subtraction is the mathematical operation of taking a larger number and reducing it to a smaller one.

Explain every step which must apply in the Subtraction of decimals.

Ans. Following steps should be followed for the subtraction of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start subtracting each corresponding digit and subtraction should start from the right side.
After subtraction make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

Explain every step which must apply in the Addition of decimals.

Ans. Following steps should be followed for the addition of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start adding each corresponding digit and addition should start from the right side.
After addition make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

Frequently Asked Questions (FAQs)

1. Explain Decimal Numbers ?

It is a number which is a combination of whole numbers and fractional numbers. Decimal numbers are presented by using points in between the numbers.

2. Explain the addition?

The process of joining two small numbers in mathematics and creating one larger number is known as an addition.

3. Explain the Subtraction ?

Subtraction is the mathematical operation of taking a larger number and reducing it to a smaller one.

4. Explain every step which must apply in the Subtraction of decimals.

Following steps should be followed for the subtraction of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start subtracting each corresponding digit and subtraction should start from the right side.
After subtraction make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

5. Explain every step which must apply in the Addition of decimals.

Following steps should be followed for the addition of decimal numbers.

Make decimal numbers similar to each other in the manner that each decimal number has an equal number of digits after the decimal. If numbers don’t have an equal number of digits after decimal then add a zero in the numbers to make it equal.
Now write one decimal number below the other and make sure that the same place value of each digit should be placed below each other.
Now start adding each corresponding digit and addition should start from the right side.
After addition make sure that the decimal must be placed at the same place from the right side as it was in both decimal numbers.

6. What's the importance of the number line in understanding decimal addition and subtraction?

A number line provides a visual representation of decimal values and operations. It helps students understand the relative sizes of decimals, the concept of negative numbers in subtraction, and the idea of addition as moving right and subtraction as moving left on the line. This visual aid can greatly enhance conceptual understanding of decimal operations.

7. What is a decimal point and why is it important in addition and subtraction?

A decimal point is a dot that separates the whole number part from the fractional part in a decimal number. It's crucial in addition and subtraction because it helps us align numbers correctly, ensuring we add or subtract corresponding place values (ones with ones, tenths with tenths, etc.).

8. What's the difference between 0.5 and 0.05 in terms of addition and subtraction?

0.5 and 0.05 are very different values. 0.5 is five-tenths (or one-half), while 0.05 is five-hundredths. In addition or subtraction, 0.5 would be aligned with the tenths place, while 0.05 would be aligned with the hundredths place, resulting in different outcomes.

9. What's the relationship between fractions and decimals in addition and subtraction?

Fractions and decimals are different representations of the same concept. Some fractions can be easily converted to decimals (like 1/2 = 0.5), making addition and subtraction simpler. Understanding this relationship can help in choosing the most efficient method for a given problem.

10. How does understanding place value help in estimating sums and differences of decimals?

Understanding place value allows you to quickly identify the most significant digits in decimal numbers. For estimation, you can round to the nearest whole number or tenth, focusing on these significant digits. This skill helps in checking if calculated answers are reasonable and in making quick mental calculations.

11. How does carrying work in decimal addition?

Carrying in decimal addition works similarly to whole number addition. When the sum in a column exceeds 9, you write down the ones digit and carry the tens digit to the next column to the left, even across the decimal point.

12. What's the difference between 0.1 + 0.2 and 0.12?

0.1 + 0.2 equals 0.3, while 0.12 is twelve-hundredths. Although they may look similar, 0.1 + 0.2 involves adding tenths, resulting in three-tenths (0.3), whereas 0.12 is already in hundredths and is less than 0.3.

13. What's the importance of estimation in decimal addition and subtraction?

Estimation is crucial in decimal operations as it helps check if your answer is reasonable. By rounding the decimals to the nearest whole number or tenth, you can quickly estimate the result and catch any major errors in your calculations.

14. How does the commutative property apply to decimal addition?

The commutative property states that the order of addends doesn't affect the sum. This applies to decimal addition as well. For example, 0.3 + 0.7 = 0.7 + 0.3 = 1.0. However, this property doesn't apply to subtraction.

15. How do you check your work in decimal addition and subtraction?

To check your work, you can use estimation, perform the inverse operation (add to check subtraction and vice versa), or use a calculator. It's also helpful to ensure your answer makes sense in the context of the problem.

16. What happens if decimal numbers have different numbers of decimal places?

If decimal numbers have different numbers of decimal places, you can add zeros after the last decimal place in the number with fewer decimal places. This doesn't change the value of the number but makes it easier to perform the operation.

17. Why do we sometimes need to "borrow" when subtracting decimals?

We "borrow" (or regroup) when subtracting decimals if the digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number). This process is similar to borrowing in whole number subtraction and ensures we can perform the subtraction correctly.

18. Can the result of subtracting two positive decimals be negative?

Yes, the result of subtracting two positive decimals can be negative if the number being subtracted (subtrahend) is larger than the number you're subtracting from (minuend). For example, 0.3 - 0.5 = -0.2.

19. How do you add or subtract mixed numbers with decimals?

To add or subtract mixed numbers with decimals, first convert the whole number part to a decimal by adding a decimal point and zeros as needed. Then, perform the addition or subtraction as usual, aligning the decimal points.

20. How do you know when to round your answer in decimal addition or subtraction?

Rounding in decimal operations often depends on the context of the problem or the level of precision required. Generally, you round to the same number of decimal places as the number with the fewest decimal places in the original problem, unless otherwise specified.

21. What's the difference between 0.25 + 0.25 and 0.25 × 2?

Both 0.25 + 0.25 and 0.25 × 2 give the same result (0.50), but they represent different operations. Addition (0.25 + 0.25) involves combining two quantities, while multiplication (0.25 × 2) involves scaling one quantity.

22. What's the importance of place value when adding or subtracting decimals with different numbers of decimal places?

Place value is crucial when working with decimals of different lengths. It ensures that you're adding or subtracting corresponding values (tenths with tenths, hundredths with hundredths, etc.). Adding zeros after the last decimal place in shorter numbers can help visualize this alignment.

23. What role does precision play in decimal addition and subtraction?

Precision in decimal operations refers to the number of decimal places in the result. Generally, the result should have the same precision as the least precise number in the problem. Understanding precision helps in rounding answers appropriately and interpreting results in real-world contexts.

24. How do you add or subtract decimals mentally?

Mental calculation with decimals often involves breaking the numbers into easier parts. For example, to add 0.8 + 0.7, you might think "0.8 + 0.2 = 1, and 0.7 - 0.2 = 0.5, so 1 + 0.5 = 1.5". Practice and understanding place value are key to improving mental math with decimals.

25. How do you explain why 0.1 + 0.2 doesn't exactly equal 0.3 in computer arithmetic?

In computer arithmetic, numbers are represented in binary (base-2) format. Some decimal fractions that are finite in base-10 become infinite repeating fractions in base-2. Due to limited precision in computers, this can lead to small rounding errors. While 0.1 + 0.2 should equal 0.3, in many programming languages it might equal 0.30000000000000004 due to these limitations.

26. How do you line up decimal numbers for addition or subtraction?

To line up decimal numbers, align the decimal points vertically. This ensures that you're adding or subtracting corresponding place values. If a number doesn't have a decimal part, you can imagine a decimal point after the ones place.

27. Can you add or subtract a whole number and a decimal number?

Yes, you can add or subtract a whole number and a decimal number. Treat the whole number as if it has a decimal point after it (e.g., 5 becomes 5.0) and then align the decimal points as usual.

28. How does place value affect decimal addition and subtraction?

Place value is crucial in decimal operations. Each column represents a specific place value (ones, tenths, hundredths, etc.). When adding or subtracting, we must ensure we're working with the same place values in each column to get the correct result.

29. How does adding or subtracting a decimal affect the position of the decimal point in the result?

The position of the decimal point in the result should align with the decimal points of the numbers being added or subtracted. The operation itself doesn't change the position of the decimal point

30. What's the role of zero in decimal addition and subtraction?

Zero plays several important roles in decimal operations: it can be a placeholder (as in 10.05), it can be added to the end of a decimal without changing its value (3.5 = 3.50), and it's crucial when borrowing across the decimal point in subtraction.

31. How do you explain why 1.000 - 0.999... (where 9 repeats infinitely) equals zero?

0.999... (where 9 repeats infinitely) is actually equal to 1. This can be proven algebraically or by considering that the difference between 1 and 0.999... is infinitesimally small. Therefore, 1.000 - 0.999... = 1 - 1 = 0. This concept touches on limits and infinite series in higher mathematics.

32. What's the connection between decimal addition/subtraction and scientific notation?

In scientific notation, numbers are expressed as a decimal between 1 and 10 multiplied by a power of 10. When adding or subtracting numbers in scientific notation, you need to ensure the exponents are the same, which often involves decimal operations. Understanding both concepts is crucial in handling very large or very small numbers in science and engineering.

33. What common mistakes do students make when subtracting decimals?

Common mistakes in decimal subtraction include misaligning decimal points, forgetting to borrow properly across the decimal point, ignoring place value, and incorrectly placing the decimal point in the answer.

34. How do you subtract a larger decimal from a smaller one?

To subtract a larger decimal from a smaller one, perform the subtraction as usual (larger number on top, smaller on bottom) and then make the result negative. For example, to calculate 0.3 - 0.5, you would do 0.5 - 0.3 = 0.2, then make the answer negative: -0.2.

35. How do you explain the concept of borrowing across the decimal point in subtraction?

Borrowing across the decimal point is similar to borrowing in whole number subtraction, but it involves place value understanding. When you borrow from the ones place to the tenths place, you're actually borrowing 10 tenths. For example, in 5.0 - 0.7, you borrow 1 from 5, making it 4, and add 10 tenths to the tenths place, making it 5.0 = 4.10. Then you can subtract 0.7 to get 3.3.

36. What's the difference between 0.3 - 0.1 and 0.3 ÷ 10?

0.3 - 0.1 is a subtraction operation that results in 0.2. It involves removing 0.1 from 0.3. On the other hand, 0.3 ÷ 10 is a division operation that results in 0.03. It involves splitting 0.3 into 10 equal parts. These are fundamentally different operations with different results.

37. What's the relationship between decimal addition/subtraction and money calculations?

Decimal addition and subtraction are directly applicable to money calculations, as currency is typically represented with two decimal places. Understanding these operations is crucial for financial literacy. For example, adding $3.50 and $2.75 is the same as adding the decimals 3.50 and 2.75.

38. How does the associative property apply to decimal addition?

The associative property states that the grouping of addends doesn't affect the sum. This applies to decimal addition as well. For example, (0.1 + 0.2) + 0.3 = 0.1 + (0.2 + 0.3) = 0.6. Understanding this property can help in simplifying complex additions.

39. What's the difference between 0.5 - 0.25 and 1/2 - 1/4?

0.5 - 0.25 and 1/2 - 1/4 represent the same operation, just in different notations. 0.5 is the decimal equivalent of 1/2, and 0.25 is the decimal equivalent of 1/4. Both operations result in 0.25 or 1/4. Understanding the relationship between fractions and decimals can make certain calculations easier.

40. How do you add or subtract repeating decimals?

Adding or subtracting repeating decimals involves aligning the decimal points and performing the operation as usual. However, the result may also be a repeating decimal. In some cases, it might be easier to convert the repeating decimals to fractions first, perform the operation, and then convert back to a decimal if needed.

41. What's the importance of understanding significant figures in decimal operations?

Significant figures indicate the precision of a measurement. In decimal addition and subtraction, the result should have the same number of decimal places as the least precise measurement. This concept is crucial in scientific calculations and real-world applications where precision matters.

42. How does adding or subtracting a small decimal (like 0.001) affect a larger number?

Adding or subtracting a small decimal like 0.001 to a larger number affects only the rightmost decimal places. For example, 10.5 + 0.001 = 10.501. Understanding this helps in appreciating the scale of numbers and the impact of small changes, which is important in many real-world applications.

43. What's the connection between decimal subtraction and finding the difference between two numbers on a number line?

Decimal subtraction can be visualized as finding the distance between two points on a number line. The difference is the length of the line segment between these points. This connection helps in understanding subtraction as a measure of distance or difference, rather than just as "taking away".

44. What's the role of decimal addition and subtraction in calculating percentages?

Decimal addition and subtraction are fundamental to percentage calculations. For example, to increase a number by 15%, you'd multiply by 1.15, which is equivalent to adding 0.15 times the original number. Similarly, decreasing by 15% involves subtracting 0.15 times the original number.

45. How do you add or subtract decimals with different units (e.g., meters and centimeters)?

To add or subtract decimals with different units, you need to convert them to the same unit first. For example, to add 1.5 m and 80 cm, you could convert 80 cm to 0.8 m, then add: 1.5 m + 0.8 m = 2.3 m. This highlights the importance of understanding unit conversions in real-world applications.

46. How does understanding decimal addition and subtraction help in working with irrational numbers like π?

While irrational numbers like π can't be expressed as exact decimals, understanding decimal operations helps in working with their approximations. For example, you might use 3.14159 as an approximation for π in calculations. Being comfortable with decimal operations allows for more precise work with these approximations.

47. What's the importance of decimal addition and subtraction in data analysis and statistics?

In data analysis and statistics, decimal addition and subtraction are crucial for calculating measures like mean, median, and standard deviation. These operations are also important in data normalization, scaling, and many other statistical procedures. Proficiency in decimal operations is therefore essential for accurate data interpretation and analysis.

48. How do you explain the concept of negative decimals in the context of subtraction?

Negative decimals can be introduced through subtraction problems where the result is less than zero. For example, 0.3 - 0.5 = -0.2. This can be visualized on a number line, where moving left past zero enters the negative territory. Understanding negative decimals is crucial for representing concepts like debt, temperature below zero, or elevation below sea level.

49. What's the relationship between decimal addition/subtraction and solving equations?

Decimal addition and subtraction are fundamental in solving equations involving decimals. For example, to solve x + 0.5 = 1.2, you'd subtract 0.5 from both sides: x = 1.2 - 0.5 = 0.7. Understanding these operations is crucial for more advanced algebraic problem-solving.

50. How does the concept of decimal addition and subtraction extend to complex numbers?

Complex numbers have a real part and an imaginary part, both of which can be decimals. When adding or sub