What is Subtracting Decimals?

S3-SA4-0074

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Subtracting decimals means taking one decimal number away from another. It's similar to subtracting whole numbers, but we need to pay close attention to the decimal point and place values.

Simple Example

Quick Example

Imagine you bought a packet of biscuits for ₹15.50 and paid with a ₹20 note. To find out how much change you should get back, you would subtract ₹15.50 from ₹20.00.

Worked Example

Step-by-Step

Let's subtract 3.45 from 7.8:

1. **Align the decimal points:** Write the numbers one below the other, making sure their decimal points are in a straight vertical line. Add zeros to the number with fewer decimal places so both numbers have the same number of digits after the decimal point.
7.80
- 3.45
------

2. **Subtract from right to left:** Start subtracting the digits in the rightmost column (hundredths place).
0 - 5: We can't subtract 5 from 0, so we need to borrow from the tens place.

3. **Borrowing:** Borrow 1 from the 8 in the tenths place. The 8 becomes 7, and the 0 in the hundredths place becomes 10.
7.7(10)
- 3.4 5
--------
5

4. **Subtract the hundredths:** Now, 10 - 5 = 5.

5. **Subtract the tenths:** Move to the tenths place. 7 - 4 = 3.

6. **Place the decimal point:** Bring down the decimal point directly below the other decimal points.

7. **Subtract the ones:** Finally, subtract the digits in the ones place. 7 - 3 = 4.

So, 7.8 - 3.45 = 4.35

Why It Matters

Understanding decimal subtraction is crucial for careers in data science, economics, and engineering, where precise calculations with measurements and money are common. For example, a data scientist might use it to find the difference in average temperatures or a physicist to calculate changes in distances.

Common Mistakes

MISTAKE: Not aligning the decimal points before subtracting. | CORRECTION: Always write the numbers vertically, ensuring the decimal points are perfectly aligned. Add trailing zeros if needed to make the number of decimal places equal.

MISTAKE: Forgetting to borrow correctly when a digit in the top number is smaller than the digit below it. | CORRECTION: Treat decimal subtraction borrowing just like whole number borrowing. When you borrow from the left, reduce that digit by one and add ten to the current digit.

MISTAKE: Placing the decimal point incorrectly in the final answer. | CORRECTION: The decimal point in the answer should always be directly below the decimal points in the numbers being subtracted.

Practice Questions

Try It Yourself

QUESTION: What is 12.75 - 4.20? | ANSWER: 8.55

QUESTION: A bucket had 8.5 litres of water. If 2.37 litres were used to water plants, how much water is left? | ANSWER: 6.13 litres

QUESTION: Riya had ₹500. She spent ₹125.50 on groceries and ₹89.75 on vegetables. How much money does she have left? | ANSWER: ₹284.75

MCQ

Quick Quiz

What is 15.6 - 7.82?

7.78

7.88

8.78

8.88

The Correct Answer Is:

To subtract 7.82 from 15.6, align the decimal points: 15.60 - 7.82. Subtracting column by column gives 7.78. Options B, C, D are incorrect due to miscalculation or incorrect alignment.

Real World Connection

In the Real World

When you check your mobile data usage, you might see you started with 1.5 GB and now have 0.85 GB left. Subtracting these (1.50 - 0.85) tells you exactly how much data you've used. Similarly, a shopkeeper uses decimal subtraction to calculate change for customers paying with cash via UPI or other digital payments.

Key Vocabulary

Key Terms

DECIMAL POINT: The dot separating the whole number part from the fractional part of a decimal number | PLACE VALUE: The value of a digit based on its position in a number | BORROWING: A technique used in subtraction when a digit is smaller than the digit below it | SUBTRAHEND: The number being subtracted | MINUEND: The number from which another number is subtracted

What's Next

What to Learn Next

Great job with subtracting decimals! Next, you can learn about 'Multiplying Decimals' and 'Dividing Decimals'. These concepts will help you perform more complex calculations with decimals in everyday situations.