Decimal Addition Format: Is 7.462 + 2.13 Properly Aligned?

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

With decimals, place value position matters more than right alignment. The decimal point shows where whole numbers end and fractional parts begin. Lining up on the right would mix up tenths, hundredths, and thousandths places!

Q: Do I need to add zeros to make the numbers the same length?

You don't have to write the zeros, but it helps! Adding trailing zeros like $2.13 \rightarrow 2.130$ makes it easier to see that place values are aligned correctly.

Q: What if one number has no decimal point?

Whole numbers have an invisible decimal point at the end. For example, 25 is really 25.000. Write the decimal point and add zeros as needed to align with the other number.

Q: Does this alignment rule apply to subtraction too?

Yes! All decimal operations (addition, subtraction) require proper alignment of decimal points and place values. The rule never changes.

Decimal Alignment with Mixed Place Values

Is the following written in the correct format?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine what is the correct writing form?

00:03 We will use long addition to find the correct way

00:07 We will write so that the decimal points are one above the other

00:13 And likewise each digit one above the other accordingly

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Is the following written in the correct format?

Step-by-step solution

To determine if the addition of decimals is set up correctly, follow these steps:

Step 1: Check the alignment of the decimal points in both numbers.
Step 2: Ensure each corresponding place value (units, tenths, hundredths, etc.) is aligned vertically.
Step 3: Look at the layout provided:
$\begin{array}{c} 7.462 \\ +\phantom{.}2.13 \\ \hline \end{array}$

The first number, $7.462$ , has three decimal places, whereas the second number, $2.13$ , has two decimal places. The decimal point in $2.13$ should be directly below the decimal point in $7.462$ . However, it appears that the digits in the tenths and hundredths place of $2.13$ are not properly aligned with $7.462$ . Hence, the addition is not aligned correctly as the decimal points are not vertically aligned.

Therefore, the addition layout is incorrect, and the solution to the problem is:

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Decimal points must be vertically aligned in addition problems
Technique: Add trailing zeros: 2.13 becomes 2.130 to match 7.462
Check: Verify each place value column aligns: 7.462 + 2.130 ✓

Common Mistakes

Avoid these frequent errors

Aligning rightmost digits instead of decimal points
Don't line up the 2 in 2.13 under the 2 in 7.462 = misaligned place values! This puts tenths under thousandths, creating wrong sums. Always align decimal points first, then add trailing zeros as needed.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct writing form:

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 position matters more than right alignment. The decimal point shows where whole numbers end and fractional parts begin. Lining up on the right would mix up tenths, hundredths, and thousandths places!

Do I need to add zeros to make the numbers the same length?

You don't have to write the zeros, but it helps! Adding trailing zeros like $2.13 \rightarrow 2.130$ makes it easier to see that place values are aligned correctly.

What if one number has no decimal point?

Whole numbers have an invisible decimal point at the end. For example, 25 is really 25.000. Write the decimal point and add zeros as needed to align with the other number.

How can I tell if my decimal addition is set up correctly?

Draw an imaginary vertical line through all decimal points. If they don't line up perfectly, the problem isn't set up correctly. Each column should contain the same place value throughout.

Does this alignment rule apply to subtraction too?

Yes! All decimal operations (addition, subtraction) require proper alignment of decimal points and place values. The rule never changes.

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