Solve: 2×100,000 + 4×10,000 + 1×10 Expanded Form Equation

Q: Why can't I just add 2+4+1 and then multiply?

Because each number has a different place value! The 2 represents hundreds of thousands, the 4 represents ten thousands, and the 1 represents tens. You must respect each place value position separately.

Q: What's the easiest way to multiply large numbers like 100,000?

Count the zeros! $ 2 \times 100,000 $ means 2 followed by 5 zeros = 200,000. This makes the multiplication much faster than writing out all the steps.

Q: How do I make sure I don't miss any zeros when adding?

Line up the numbers by place value columns:200,000 40,000 10This way you can see exactly where each digit belongs!

Q: What if there are missing place values like hundreds or thousands?

That's totally normal! In this problem, there are no hundreds, thousands, or ones, so those places stay as zeros in your final answer. The expanded form only shows the non-zero place values.

Q: Is there a pattern to expanded form problems?

Yes! Always follow multiply first, then add. Each term tells you exactly: [how many] × [which place value]. Handle each piece separately, then combine at the end.

Q: How can I double-check my final answer?

Convert your answer back to expanded form! $ 240,010 = 2×100,000 + 4×10,000 + 0×1,000 + 0×100 + 1×10 + 0×1 $. If it matches the original problem, you're correct! ✓

Place Value Operations with Expanded Form

Complete the following equation:

$2\times100,000+4\times10,000+1\times10=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following equation:

$2\times100,000+4\times10,000+1\times10=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Multiply each given coefficient by its corresponding power of ten:
$2 \times 100,000 = 200,000$
$4 \times 10,000 = 40,000$
$1 \times 10 = 10$
Step 2: Add the products obtained from Step 1 together:
$200,000 + 40,000 + 10 = 240,010$

By following these steps, we find that the sum of the given terms is $240,010$ .

Therefore, the solution to the problem is $240,010$ .

Final Answer

$240,010$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply each coefficient by its corresponding place value first
Technique: Calculate separately: 2×100,000=200,000, then 4×10,000=40,000, then 1×10=10
Check: Add results step by step: 200,000+40,000+10=240,010 ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients before multiplying by place values
Don't add 2+4+1=7 first and then multiply by place values = completely wrong answer! This ignores that each coefficient belongs to a different place value position. Always multiply each coefficient by its specific place value before adding anything together.

Practice Quiz

Test your knowledge with interactive questions

If you use all of the units shown below and place them in the table, then what number do they make?

Write the values in the place value chart and convert into a number.

FAQ

Everything you need to know about this question

Why can't I just add 2+4+1 and then multiply?

Because each number has a different place value! The 2 represents hundreds of thousands, the 4 represents ten thousands, and the 1 represents tens. You must respect each place value position separately.

What's the easiest way to multiply large numbers like 100,000?

Count the zeros! $2 \times 100,000$ means 2 followed by 5 zeros = 200,000. This makes the multiplication much faster than writing out all the steps.

How do I make sure I don't miss any zeros when adding?

Line up the numbers by place value columns:

200,000
40,000
10

This way you can see exactly where each digit belongs!

What if there are missing place values like hundreds or thousands?

That's totally normal! In this problem, there are no hundreds, thousands, or ones, so those places stay as zeros in your final answer. The expanded form only shows the non-zero place values.

Is there a pattern to expanded form problems?

Yes! Always follow multiply first, then add. Each term tells you exactly: [how many] × [which place value]. Handle each piece separately, then combine at the end.

How can I double-check my final answer?

Convert your answer back to expanded form! $240,010 = 2×100,000 + 4×10,000 + 0×1,000 + 0×100 + 1×10 + 0×1$ . If it matches the original problem, you're correct! ✓

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