Calculate the Sum: 103.8 + 96.4 Decimal Addition

Decimal Addition with Carrying Across Places

103.8+96.4= 103.8+96.4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together.
00:08 First, line up the numbers. Decimal points should match.
00:13 Great! Now, add the smallest digits first.
00:22 Write down the ones digit. If you need to, carry the 1 above.
00:34 Now, add 1 to your next calculation.
00:43 Again, write down the ones digit. Remember to carry if needed.
00:48 Add 1 to your new total.
00:56 Don't forget to carry the 1 if needed as you go.
01:04 Almost done! Add, carry if you must, and finish the calculation.
01:14 Good job! That's how you solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

103.8+96.4= 103.8+96.4=

2

Step-by-step solution

To solve the problem of adding 103.8 103.8 and 96.4 96.4 , follow these steps:

  • Step 1: Write the numbers vertically, aligning the decimal points:

  • 103.8
    + 96.4

  • Step 2: Start from the rightmost digit (the tenths place) and add:

  • 8+4=128 + 4 = 12. Write down 2 in the tenths place and carry over 1 to the units place.

  • Step 3: Add the units place:

  • 3+6=93 + 6 = 9, and add the carry-over of 1: 9+1=109 + 1 = 10. Write down 0 in the units place and carry over 1 to the tens place.

  • Step 4: Add the tens place:

  • 0+9=90 + 9 = 9, and add the carry-over of 1: 9+1=109 + 1 = 10. Write down 0 in the tens place and carry over 1 to the hundreds place.

  • Step 5: Add the hundreds place:

  • 1+0=11 + 0 = 1, and add the carry-over of 1: 1+1=21 + 1 = 2. Write down 2 in the hundreds place.

  • Step 6: Write the final sum:

  • The resulting sum is 200.2 200.2 .

Thus, the calculated sum of 103.8 103.8 and 96.4 96.4 is 200.2 200.2 .

The answer choice corresponding to this result is: 200.2

3

Final Answer

200.2

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Always line up decimal points vertically before adding
  • Technique: Add right to left: 8 + 4 = 12, carry 1
  • Check: Count decimal places: both have 1, so answer has 1 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't add 103.8 + 96.4 by treating them as whole numbers = 1002! This ignores place value completely and gives massive errors. Always align decimal points first, then add column by column.

Practice Quiz

Test your knowledge with interactive questions

\( \text{0.6+0}.5= \)

+=

FAQ

Everything you need to know about this question

Why do I need to align the decimal points?

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Aligning decimal points ensures you're adding like place values: tenths to tenths, ones to ones, tens to tens. Without alignment, you'd be adding numbers in the wrong places!

What happens when I carry over from the decimal places?

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Carrying works the same way! When 8+4=12 8 + 4 = 12 in the tenths place, write down 2 and carry the 1 to the ones place. The decimal point stays in its position.

How do I know where to put the decimal point in my answer?

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The decimal point in your answer goes directly below the aligned decimal points in the problem. It never moves during addition!

What if the numbers have different amounts of decimal places?

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Add zeros to make them equal! For example, 12.5+8.73 12.5 + 8.73 becomes 12.50+8.73 12.50 + 8.73 . This helps with alignment and prevents mistakes.

Can I check my work without redoing the whole problem?

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Yes! Try rounding first: 104+96=200 104 + 96 = 200 . Since your answer 200.2 200.2 is very close to 200, it's likely correct!

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