Decimal Subtraction Format: Is 25.754 - 3.13 Properly Aligned?

Q: What if the numbers have different amounts of decimal places?

That's totally normal! Just add zeros to the shorter decimal to make them match. For example, treat $3.13$ as $3.130$ so it has the same number of decimal places as $25.754$.

Q: Why can't I just line up the numbers from the right side?

Because that would put digits in the wrong place values! In $25.754 - 3.13$, if you line up from the right, you'd try to subtract 3 from 4 in the thousandths place, which is completely wrong.

Q: Do I need to write the zeros when I add them?

It's helpful but not required. Writing $3.130$ instead of $3.13$ makes the alignment clearer, but as long as your decimal points line up, the math works the same way.

Q: How do I know if my decimal alignment is correct?

Check that the decimal points are directly above and below each other. Each column should contain digits from the same place value: units with units, tenths with tenths, etc.

Decimal Alignment with Vertical Subtraction

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 format?

00:04 We will use long subtraction to find the correct way

00:10 We will write so that the decimal points are one above the other

00:16 And likewise each digit should be one above the other accordingly

00:22 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Is the following written in the correct format?

Step-by-step solution

When setting up a subtraction problem with decimals, it is crucial that the decimal points in both numbers directly align. This ensures that each digit is correctly placed in its respective place value column (units, tenths, hundredths, etc.) to facilitate accurate subtraction.

In this problem, the number $25.754$ is aligned vertically with $3.13$ . Upon inspection, both decimals are indeed arranged vertically so that the decimal points are in the same column. The digits following the decimal in $3.13$ are tenths and hundredths, leaving the thousandths position empty, which is acceptable as we can treat the missing place value as zero for alignment purposes (i.e., treat $3.13$ as $3.130$ ).

Therefore, the numbers are set up correctly for vertical subtraction, where:

\begin{array}{c} 25.754 \\ -\,3.130 \\ \hline \end{array}

This alignment confirms that the subtraction operation can reliably proceed as the format is correct.

Therefore, the correct answer to the problem is Yes.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Decimal points must line up vertically in column format
Technique: Treat $3.13$ as $3.130$ to match place values
Check: Units, tenths, hundredths, thousandths all align properly ✓

Common Mistakes

Avoid these frequent errors

Aligning numbers by their rightmost digits instead of decimal points
Don't line up 25.754 and 3.13 by their last digits = completely wrong subtraction! This puts digits in wrong place value columns, making 4 subtract from 3. Always align decimal points first, then add zeros if needed.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct writing form:

FAQ

Everything you need to know about this question

What if the numbers have different amounts of decimal places?

That's totally normal! Just add zeros to the shorter decimal to make them match. For example, treat $3.13$ as $3.130$ so it has the same number of decimal places as $25.754$ .

Why can't I just line up the numbers from the right side?

Because that would put digits in the wrong place values! In $25.754 - 3.13$ , if you line up from the right, you'd try to subtract 3 from 4 in the thousandths place, which is completely wrong.

Do I need to write the zeros when I add them?

It's helpful but not required. Writing $3.130$ instead of $3.13$ makes the alignment clearer, but as long as your decimal points line up, the math works the same way.

How do I know if my decimal alignment is correct?

Check that the decimal points are directly above and below each other. Each column should contain digits from the same place value: units with units, tenths with tenths, etc.

What happens if I forget to align the decimal points?

You'll get a completely wrong answer! Misaligned decimals put digits in wrong place values, so you might subtract hundredths from thousandths or units from tenths. Always check your alignment before calculating.

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