Mathematical Notation: Identifying Correct Writing Forms

Decimal Addition with Proper Alignment

Choose the correct writing form:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:02 Let's figure out the correct way to write this.
00:06 We'll use long addition to find the right format.
00:11 Line up the decimal points, one directly above the other.
00:16 Make sure each digit is aligned correctly, too.
00:20 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the correct writing form:

2

Step-by-step solution

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

  • Step 1: Align the decimal numbers by their decimal points.
  • Step 2: Check if each digit is correctly aligned with its corresponding digit based on place value.
  • Step 3: Ensure the operation symbol is properly placed.

Now, let's work through each step:
Step 1: Start with the number 13.45 and align 3.21 directly below it such that the decimal points are vertically aligned. This ensures that the tenths, hundredths, and whole numbers are in the correct columns.
Step 2: Verify that: - The '1' in 13.45 is in the tens place, and the '3' in 3.21 is in the ones place, both aligned left of the decimal. - The '3' in 13.45 and '2' in 3.21 are aligned in the tenths column. - The '4' in 13.45 and '1' in 3.21 are in the hundredths column.
Step 3: Place the '+' sign outside and to the left, in line with the numbers, ensuring it is clearly indicating addition.

Therefore, the correct alignment for the addition of these decimal numbers is:

13.453.21+

3

Final Answer

13.453.21+

Key Points to Remember

Essential concepts to master this topic
  • Alignment Rule: Always line up decimal points vertically before adding
  • Technique: Place 13.45 above 3.21 with decimals aligned in columns
  • Check: Verify each digit sits in correct place value column ✓

Common Mistakes

Avoid these frequent errors
  • Aligning numbers by their rightmost digits instead of decimal points
    Don't line up 13.45 and 3.21 by their last digits = wrong place values! This puts tenths in hundredths column and gives incorrect sums. Always align the decimal points first, then check that each digit is in its proper place value column.

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 from the right like with whole numbers?

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With decimals, place value is everything! The decimal point shows where ones end and tenths begin. If you align from the right, you're putting digits in wrong columns and your answer will be completely off.

What if the decimal numbers have different lengths?

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No problem! Align the decimal points first, then imagine invisible zeros at the end of shorter numbers. For example, treat 13.45 as 13.450 when adding to 3.210.

Where should I put the plus sign?

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Place the plus sign to the left of the bottom number, clearly showing it's addition. Make sure it doesn't interfere with the number alignment.

How do I know if my alignment is correct?

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Check that each column contains digits of the same place value: tens with tens, ones with ones, tenths with tenths, and hundredths with hundredths!

What happens if I align wrong?

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Wrong alignment = wrong answer! For example, if you misalign 13.45 + 3.21, you might get 45.66 instead of 16.66. Always double-check your decimal point placement.

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