Solve Decimal Addition: 0.77 + 30.6 in Vertical Format

Decimal Addition with Place Value Alignment

0.7730.6+

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Add 0 in missing digits, place the decimal point
00:08 First add the smallest digits
00:11 Substitute, and continue adding
00:21 Calculate and place the ones, remember 1 above
00:30 Add 1 to this calculation
00:39 Substitute, and continue to add, calculate and place accordingly
00:49 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

0.7730.6+

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Align the numbers 0.770.77 and 30.630.6 by their decimal points:
    30.6+  0.77 \begin{aligned} 30&.6 \\ + ~~ 0&.77 \\ \hline \end{aligned}

  • Step 2: Add these numbers starting from the rightmost digit, considering each place value.

  • Adding hundredths place:
    0+7=70 + 7 = 7

  • Adding tenths place:
    6+7=136 + 7 = 13, write down 33 and carry over 1 to the next column.

  • Adding whole number and carry over:
    0+1+30=310 + 1 + 30 = 31

  • Thus, the sum is 31.3731.37.

Therefore, the solution to the problem is 31.3731.37.

3

Final Answer

31.37

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points vertically before adding digits
  • Technique: Add 0.77 + 30.6 by treating 30.6 as 30.60
  • Check: Count decimal places: 2 places in both numbers = 2 in answer ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't line up the rightmost digits like whole numbers = wrong place values! This puts tenths with hundredths and gives answers like 38.3 instead of 31.37. Always align the decimal points vertically first.

Practice Quiz

Test your knowledge with interactive questions

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

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FAQ

Everything you need to know about this question

Why do I need to add a zero to 30.6?

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Adding zeros to the right of decimals doesn't change the value! 30.6=30.60 30.6 = 30.60 helps you see that there are 0 hundredths to add to the 7 hundredths in 0.77.

What if the decimal points don't line up naturally?

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That's exactly when alignment is most important! Write the numbers in vertical format with decimal points directly above and below each other, like a column.

Do I always carry over when adding decimals?

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Yes! The same carrying rules apply. When 6+7=13 6 + 7 = 13 in the tenths place, write 3 and carry the 1 to the ones place, just like with whole numbers.

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

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The decimal point in your answer goes in the same column as the decimal points in the problem. It lines up vertically with the others!

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

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Add zeros to make them equal! For example, if adding 2.5 + 1.23, write it as 2.50+1.23 2.50 + 1.23 so both have 2 decimal places.

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