Calculate the Sum: 2.16 + 3.214 Decimal Addition

Q: Why do I need to add a zero to 2.16?

Adding zeros helps you align the place values correctly! $ 2.16 $ becomes $ 2.160 $ so the thousandths place lines up with $ 3.214 $.

Q: What if I forget to line up the decimal points?

You'll get the wrong answer! For example, if you add $ 216 + 3214 = 3430 $ and randomly place a decimal, you might get 34.30 instead of the correct 5.374.

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

The decimal point in your answer goes directly below the decimal points in the problem. If you line them up correctly, the answer's decimal point will be in the right place automatically!

Q: Can I add decimals from left to right instead?

It's better to add from right to left like with whole numbers. This way, if you need to carry over (like $ 7 + 8 = 15 $), you're following the natural flow of addition.

Q: What if the decimals have different numbers of digits?

No problem! Just add zeros to the shorter decimal to match the longer one. For instance, $ 4.5 + 2.367 $ becomes $ 4.500 + 2.367 $.

Decimal Addition with Different Place Values

$2.16+3.214=$

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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 We'll use vertical addition to find the answer.

00:12 Make sure to align the numbers with the decimal points lined up.

00:17 First, add the smallest digits on the right.

00:24 Compute the sum and write the result below.

00:34 Keep adding, and writing down the results step by step.

01:00 And there you have it! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2.16+3.214=$

Step-by-step solution

To find the sum of $2.16$ and $3.214$ , follow these steps:

First, write the numbers vertically, aligning them by their decimal points:

$\phantom{00}2.160$
$+3.214$
$\_\_\_\_\_\_$

Add the numbers from right to left, adding zeros if necessary to balance the number of decimal places:

Start from the rightmost digit: $0 + 4 = 4$ .
Next column to the left: $6 + 1 = 7$ .
Next column to the left: $1 + 2 = 3$ .
Finally, add the whole number part: $2 + 3 = 5$ .
Combine the results to get the final sum.

Therefore, the sum of $2.16$ and $3.214$ is $\textbf{5.374}$ .

Final Answer

5.374

Key Points to Remember

Essential concepts to master this topic

Alignment: Always line up decimal points vertically when adding
Technique: Add zeros to match decimal places: 2.16 becomes 2.160
Check: Count decimal places in answer matches the longest addend ✓

Common Mistakes

Avoid these frequent errors

Not aligning decimal points properly
Don't line up the rightmost digits instead of decimal points = 6.374 instead of 5.374! This misaligns place values and gives completely wrong answers. Always align the decimal points first, then add zeros if needed.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to add a zero to 2.16?

Adding zeros helps you align the place values correctly! $2.16$ becomes $2.160$ so the thousandths place lines up with $3.214$ .

What if I forget to line up the decimal points?

You'll get the wrong answer! For example, if you add $216 + 3214 = 3430$ and randomly place a decimal, you might get 34.30 instead of the correct 5.374.

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

The decimal point in your answer goes directly below the decimal points in the problem. If you line them up correctly, the answer's decimal point will be in the right place automatically!

Can I add decimals from left to right instead?

It's better to add from right to left like with whole numbers. This way, if you need to carry over (like $7 + 8 = 15$ ), you're following the natural flow of addition.

What if the decimals have different numbers of digits?

No problem! Just add zeros to the shorter decimal to match the longer one. For instance, $4.5 + 2.367$ becomes $4.500 + 2.367$ .

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