Decimal Addition Check: Verifying 312.54 + 1203.22 Alignment

Decimal Addition with Proper Alignment

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

312.54+1203.22

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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 placement is correct?
00:03 We'll use long addition to find the position of the decimal point
00:10 In long addition, the decimal points must be aligned one above the other
00:26 In our exercise, the decimal points are not aligned one above the other
00:34 Therefore, the decimal point placement is incorrect
00:37 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.

312.54+1203.22

2

Step-by-step solution

To determine if the addition problem is set up correctly, we need to analyze how the numbers are aligned.

The given numbers for addition are 312.54312.54 and 1203.221203.22. When aligning these numbers for addition:

312.54+1203.22\begin{array}{r} 312.54 \\ +1203.22 \\ \hline \end{array}

We examine how the decimal points are positioned. For a correct setup, the decimal points should be aligned vertically. However, in the visual provided:

  • The decimal point in 312.54312.54 is positioned one place to the right compared to the decimal in 1203.221203.22.

  • The alignment should have appeared as 00312.54+1203.22 \begin{aligned} &\phantom{00}312.54 \\ &+1203.22 \end{aligned} to be correct, but it does not.

Since the decimal points are not vertically aligned, the addition is set up incorrectly.

Therefore, the statement regarding the positioning of the decimal points is Not true.

3

Final Answer

Not true

Key Points to Remember

Essential concepts to master this topic
  • Rule: Decimal points must line up vertically in addition
  • Technique: Add zeros if needed: 312.54 becomes 0312.54 under 1203.22
  • Check: Count decimal places: both numbers have 2, answer should too ✓

Common Mistakes

Avoid these frequent errors
  • Aligning numbers by their rightmost digits instead of decimal points
    Don't line up 312.54 and 1203.22 by their last digits = wrong place values! The 4 in 312.54 represents hundredths, but gets treated as units. Always align decimal points vertically first, then add from right to left.

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?

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Because decimal numbers have different place values! When you align from the right, you're adding tenths to hundredths, which gives the wrong answer. The decimal point shows where whole numbers end and fractions begin.

What if one number has more decimal places than the other?

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Add trailing zeros to make them equal! For example, if adding 12.5 + 3.47, write it as 12.50 + 3.47. This doesn't change the value but helps with alignment.

How do I know if my decimal addition setup is correct?

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Check that the decimal points form a straight vertical line. If they're not aligned, your answer will be wrong by factors of 10, 100, or more!

Can I ignore the decimal points and add them back later?

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No! This leads to major errors. The decimal point's position determines the value of each digit. Always keep decimal points aligned throughout the entire process.

What happens if I misalign by one place?

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Your answer will be 10 times too big or too small! For example, 312.54+1203.22=1515.76312.54 + 1203.22 = 1515.76, but with misalignment you might get 15157.6 or 151.576.

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