Decimal Point Position Analysis in Vertical Subtraction

Decimal Alignment with Vertical Subtraction

Determine whether the exercise is correctly written or not.
The position of the decimal point corresponds.

38.15-122.3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine if the decimal point position matches?
00:03 We'll use long addition to find the position of the decimal point
00:07 In long addition, the decimal points must be aligned one above the other
00:13 In our exercise, the decimal points are aligned one above the other
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine whether the exercise is correctly written or not.
The position of the decimal point corresponds.

38.15-122.3

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Ensure the decimal numbers are aligned correctly according to their decimal points.

  • Perform the arithmetic operation to verify logical correctness.

Let's analyze the given numbers:

  • The first number is 38.1538.15.

  • The second number is 122.3122.3. We can express this as 122.30122.30 to simplify alignment.

Align the numbers vertically based on their decimal points:

38.15 \quad 38.15
122.30 -122.30

Notice the decimal points are aligned. Now, perform the subtraction:

Start from the rightmost column:

  • (50=5) (5 - 0 = 5)

  • (13=Borrow 10, becomes 113=8) (1 - 3 = \text{Borrow } 10, \text{ becomes } 11 - 3 = 8)

Move to the next left column (tens column):

  • (borrowed 18 becomes 7) (\text{borrowed } 1 \rightarrow 8 \text{ becomes } 7)

  • (72=5) (7 - 2 = 5)

  • (32=1) (3 - 2 = 1)

  • (The result is negative because 38.15 is less than 122.30) (\text{The result is negative because 38.15 is less than 122.30})

Result of the subtraction is 84.15 -84.15 .

Since the exercise primarily asks if the decimal points are aligned correctly, and they indeed align correctly, we conclude:

The exercise is written correctly with respect to decimal alignment.

Therefore, the solution to the problem is True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Alignment Rule: Decimal points must line up vertically for proper subtraction
  • Technique: Add zeros to match decimal places: 122.3 becomes 122.30
  • Check: Verify decimal points align before calculating: 38.15 vs 122.30 ✓

Common Mistakes

Avoid these frequent errors
  • Misaligning decimal points when setting up vertical subtraction
    Don't line up the rightmost digits without considering decimal points = completely wrong answer! This treats 38.15 and 122.3 as if they were 3815 and 1223. Always align decimal points vertically first, then add zeros as needed.

Practice Quiz

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FAQ

Everything you need to know about this question

Why can't I just line up the numbers on the right like with whole numbers?

+

With decimals, place value matters! The digit 5 in 38.15 represents hundredths, while 3 in 122.3 represents tenths. Lining them up would be like adding apples and oranges!

Do I need to add zeros to make the decimal places equal?

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Yes! Adding zeros helps you see the alignment clearly. 122.3122.3 becomes 122.30122.30 so both numbers have two decimal places.

What if one number doesn't have a decimal point?

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Treat whole numbers as having a decimal point at the end. For example, 45 becomes 45.00 when working with numbers like 12.75.

How do I know if my decimal alignment is correct?

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Draw an imaginary vertical line through all the decimal points. If they all line up on this line, your setup is correct!

Does the sign affect decimal alignment?

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No! Whether it's addition or subtraction, the decimal alignment rules stay the same. Always line up those decimal points first.

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