Solve Decimal Addition: 30.07 + 6.06 Step-by-Step

Decimal Addition with Place Value Alignment

30.076.06+

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

30.076.06+

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Align the decimal numbers vertically.
  • Step 2: Ensure the decimal points line up correctly.
  • Step 3: Add the numbers starting from the hundredths place, then the tenths, whole numbers, carrying over any extra values if necessary.

Now, let's work through each step:

Step 1: Align the numbers vertically:

+30.07+006.06 \begin{array}{c} \phantom{+}30.07 \\ + \phantom{00}6.06 \\ \hline \end{array}

Step 2: Add the numbers starting from the rightmost place (hundredths position):

  • Hundredths: 7+6=137 + 6 = 13, place 3 and carry over 1.
  • Tenths: 0+0+1=10 + 0 + 1 = 1.

Next, move to the whole numbers:

  • Units: 0+6=60 + 6 = 6.
  • Then, tens: 3+0=33 + 0 = 3.

The final sum is:

+30.07+006.06+36.13 \begin{array}{c} \phantom{+}30.07 \\ + \phantom{00}6.06 \\ \hline \phantom{+}36.13 \\ \end{array}

Therefore, the solution to the problem is 36.1336.13.

3

Final Answer

36.13

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points vertically before adding numbers
  • Technique: Add from right to left: 7+6=13 7 + 6 = 13 , write 3, carry 1
  • Check: Count decimal places: both numbers have 2, so answer has 2 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't just line up the numbers from the right without considering decimal points = wrong place values! This makes you add tenths to hundredths or units to tenths, giving completely wrong answers. Always line up the decimal points first, then add column by column.

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 line up the decimal points?

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Lining up decimal points ensures you're adding the same place values together! Just like in regular addition, you add ones to ones, tens to tens - with decimals, you add tenths to tenths and hundredths to hundredths.

What do I do when I get a number bigger than 9 in a column?

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When adding gives you 10 or more (like 7+6=13 7 + 6 = 13 ), write down the ones digit and carry the tens digit to the next column to the left. It's just like regular addition!

How many decimal places should my answer have?

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Your answer should have the same number of decimal places as the numbers you're adding. Since both 30.07 and 6.06 have 2 decimal places, your answer should too!

What if the decimal points don't line up when I write them?

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Make sure you're writing the numbers vertically with decimal points directly under each other. You can add zeros to the right if needed - 30.07 is the same as 30.070.

Can I add decimals without lining them up?

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It's much harder and more error-prone! While possible, always line up decimal points - it's the safest and clearest method that works every time.

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