Place Value Addition: Finding Components of 41 Using Hundreds, Tens, and Units

Q: Why is the 4 worth 400 and not just 4?

Because the 4 is in the hundreds place! Each position has a different value: hundreds (×100), tens (×10), and units (×1). The digit 4 in hundreds place means 4 groups of 100.

Q: What if there's no number in the units column?

That means there are zero units, so you add 0 to your sum. For example, 410 has 4 hundreds, 1 ten, and 0 units: 400 + 10 + 0 = 410.

Q: How do I know which column is which?

Start from the right! The rightmost column is always units (ones), then tens, then hundreds as you move left. Remember: Units-Tens-Hundreds from right to left.

Q: Can I just ignore the zeros?

In the final addition, yes! But always identify them first. This shows you understand that some place values are empty, which is important for larger numbers.

Q: What's the difference between 41 and 410?

41 has no hundreds (4 tens + 1 unit), while 410 has 4 hundreds and 1 ten. The position of each digit completely changes its value!

Place Value Decomposition with Three-Digit Numbers

Choose the addition exercise using hundreds + tens + units that results in the number shown below:

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the addition exercise using hundreds + tens + units that results in the number shown below:

Step-by-step solution

To solve this problem, let's analyze each step:

Step 1: Identify the given information.
- We are tasked to find an addition expression using hundreds + tens + units that equals the number depicted, which is 410.
Step 2: Recognize place values from given information.
- Hundreds column indicates the numeral 4, which denotes 400.
- Tens column indicates the numeral 1, which denotes 10.
Step 3: Perform the addition.
- Combine 400 (from Hundreds) + 10 (from Tens) + 0 (implied from Units) which results in 410.
- Therefore, the resulting sum is $400 + 10 = 410$ .

The correct choice, which gives us exactly 410, shows that $400 + 10 = 410$ .

Therefore, the solution to the problem is:

$400+10=410$

Final Answer

$400+10=410$

Key Points to Remember

Essential concepts to master this topic

Rule: Each digit's value equals digit × position value
Technique: 4 in hundreds = 400, 1 in tens = 10
Check: Add components back together: 400 + 10 + 0 = 410 ✓

Common Mistakes

Avoid these frequent errors

Reading digits as their face value instead of place value
Don't read 4 as just 4 and 1 as just 1 = wrong sum of 5! The position determines the true value. Always multiply each digit by its place value: 4 × 100 + 1 × 10 + 0 × 1.

Practice Quiz

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What number do the blue squares below represent?

FAQ

Everything you need to know about this question

Why is the 4 worth 400 and not just 4?

Because the 4 is in the hundreds place! Each position has a different value: hundreds (×100), tens (×10), and units (×1). The digit 4 in hundreds place means 4 groups of 100.

What if there's no number in the units column?

That means there are zero units, so you add 0 to your sum. For example, 410 has 4 hundreds, 1 ten, and 0 units: 400 + 10 + 0 = 410.

How do I know which column is which?

Start from the right! The rightmost column is always units (ones), then tens, then hundreds as you move left. Remember: Units-Tens-Hundreds from right to left.

Can I just ignore the zeros?

In the final addition, yes! But always identify them first. This shows you understand that some place values are empty, which is important for larger numbers.

What's the difference between 41 and 410?

41 has no hundreds (4 tens + 1 unit), while 410 has 4 hundreds and 1 ten. The position of each digit completely changes its value!

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