Verify Decimal Subtraction Setup: 38.15 - 122.3 Alignment Check

Decimal Alignment with Mixed Place Values

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 subtraction to find the position
00:09 In long subtraction, the decimal points must be aligned one above the other
00:14 In our exercise, the points are not aligned one above the other,
00:21 Therefore the decimal point position is incorrect
00:24 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 determine whether the exercise is set correctly, we need to align the decimal points of the two numbers involved in the subtraction operation:

1. The given numbers are 38.15 and 122.3.
2. We write them down vertically, aligning by the decimal points:

038.150122.3 \begin{array}{c} \hphantom{0}38.15 \\ - \hphantom{0}122.3 \\ \end{array}

3. Notice that the number 38.15 has two decimal places (hundredths), while 122.3 only has one decimal place (tenths). Therefore, the hundredths place in 122.3 is effectively considered as "0" to match the decimal places of the first number. Upon aligning the decimal points, 38.15 and 122.3 indeed match as:

038.15122.30 \begin{array}{c} \hphantom{0}38.15 \\ - 122.30 \\ \end{array}

4. This check confirms that there is an incorrect statement regarding "The position of the decimal point corresponds," as the numbers are aligned at the decimal points considering all decimal places are consistently represented.

Therefore, the statement "The position of the decimal point corresponds" is Not true.

3

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic
  • Rule: Decimal points must align vertically in subtraction problems
  • Technique: Add zeros to match decimal places: 122.3 becomes 122.30
  • Check: Count decimal places in both numbers are equal ✓

Common Mistakes

Avoid these frequent errors
  • Aligning numbers by rightmost digit instead of decimal point
    Don't line up 38.15 and 122.3 by their last digits = wrong place values! This puts tenths under hundredths and creates calculation errors. Always align the 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 from the right side like with whole numbers?

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With decimals, place value matters! The decimal point shows where whole numbers end and fractions begin. Aligning from the right would put tenths under hundredths, giving you the wrong answer.

Do I need to add zeros when the decimal places don't match?

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Yes! Adding zeros helps you see the alignment clearly. 122.3 is the same as 122.30 - the zero doesn't change the value but makes subtraction easier.

What happens if I don't align the decimal points correctly?

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You'll get the wrong answer because you're subtracting from the wrong place values. For example, you might subtract hundredths from tenths instead of hundredths from hundredths.

How do I know if my decimal alignment is correct?

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Look for these signs:

  • Decimal points form a straight vertical line
  • Both numbers have the same number of decimal places
  • Each digit column represents the same place value

Can I solve this problem even though 38.15 is smaller than 122.3?

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Absolutely! The result will be negative (-84.15), but the alignment rules stay the same. Proper decimal alignment works for any subtraction problem.

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