What is the Difference of Decimals?

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Grade Level:

Class 3

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The difference of decimals means finding how much larger one decimal number is than another. It's essentially subtracting one decimal number from another to find the leftover amount.

Simple Example

Quick Example

Imagine you bought a packet of biscuits for Rs 15.50 and a juice box for Rs 10.25. To find out how much more the biscuits cost than the juice, you would find the difference between 15.50 and 10.25.

Worked Example

Step-by-Step

Let's subtract 5.75 from 12.30.

Step 1: Write the numbers one below the other, aligning the decimal points. Make sure the larger number is on top.
12.30
- 5.75
-------

Step 2: Start subtracting from the rightmost digit (hundredths place).
12.3(0)
- 5.7(5)
We can't subtract 5 from 0, so we borrow from the tens place (3 becomes 2, 0 becomes 10). 10 - 5 = 5.

Step 3: Move to the tenths place.
12.(2)(10)
- 5.(7)5
Now we have 2 in the tenths place. We can't subtract 7 from 2, so we borrow from the ones place (2 becomes 1, 2 becomes 12). 12 - 7 = 5.

Step 4: Move to the ones place.
1(1).(12)(10)
- (5).75
Now we have 1 in the ones place. We can't subtract 5 from 1, so we borrow from the tens place (1 becomes 0, 1 becomes 11). 11 - 5 = 6.

Step 5: Bring down the decimal point straight down.
11.55

Step 6: The tens place (leftmost digit) is 0, so there's nothing left to subtract.

Answer: The difference is 6.55.

Why It Matters

Understanding decimal differences is crucial for everyday calculations like managing money, measuring ingredients, or checking cricket scores. It's used by scientists to compare data, by engineers to design precise parts, and by economists to analyze financial changes.

Common Mistakes

MISTAKE: Not aligning the decimal points properly before subtracting. | CORRECTION: Always make sure the decimal points are directly one above the other. This ensures you subtract digits from the correct place value.

MISTAKE: Forgetting to add zeros to the end of a decimal number to make the number of decimal places equal. | CORRECTION: If one number has fewer decimal places, add trailing zeros so both numbers have the same number of digits after the decimal point (e.g., 7.5 becomes 7.50).

MISTAKE: Not borrowing correctly when a digit is smaller than the one below it. | CORRECTION: Remember to 'borrow' from the digit to its left, reducing that digit by one and adding ten to the current digit.

Practice Questions

Try It Yourself

QUESTION: What is 9.75 - 3.20? | ANSWER: 6.55

QUESTION: A tailor had 25.5 meters of cloth. He used 12.75 meters for a dress. How much cloth is left? | ANSWER: 12.75 meters

QUESTION: You have Rs 50.00. You buy a notebook for Rs 18.50 and a pen for Rs 7.25. How much money do you have left? (Hint: First find the total cost of items, then subtract from Rs 50.00) | ANSWER: Rs 24.25

MCQ

Quick Quiz

What is the difference between 8.5 and 3.25?

5.75

5.25

11.75

5.35

The Correct Answer Is:

To find the difference, subtract 3.25 from 8.50 (after adding a zero to 8.5). 8.50 - 3.25 = 5.25. Option B is correct.

Real World Connection

In the Real World

When you check your mobile phone bill, you might see that you used 5.3 GB of data out of a 10 GB plan. To know how much data is remaining, you find the difference between 10.0 and 5.3. Similarly, shopkeepers use this daily to calculate change for customers paying with cash.

Key Vocabulary

Key Terms

DECIMAL POINT: A dot that separates the whole number part from the fractional part of a number | PLACE VALUE: The value of a digit based on its position in a number | SUBTRACTION: The process of taking one number or amount away from another | BORROWING: A technique used in subtraction when a digit in the top number is smaller than the digit below it

What's Next

What to Learn Next

Great job learning about subtracting decimals! Next, you can explore 'Multiplying Decimals' and 'Dividing Decimals'. These will help you perform even more complex calculations with decimal numbers, which are super useful in real life!