Solve: 6×100,000 + 4×10,000 + 2×1,000 + 7 Expanded Form Equation

Q: Do I need to multiply 7×1 or can I just write 7?

You should write $ 7 \times 1 = 7 $ to show you understand place value. The ones place has a value of 1, so every digit gets multiplied by its place value.

Q: What if I get confused by all the zeros?

Count carefully! 100,000 has 5 zeros, 10,000 has 4 zeros, 1,000 has 3 zeros. When you multiply, you keep the same number of zeros: 6×100,000 = 600,000 (still 5 zeros).

Q: How can I check if 642,007 is correct?

Break it down by place value! 642,007 = 6 hundred-thousands + 4 ten-thousands + 2 thousands + 0 hundreds + 0 tens + 7 ones. This matches our original expanded form perfectly!

Expanded Form with Place Value Computation

Solve the following equation:

$6\times100,000+4\times10,000+2\times1,000+7\times1=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$6\times100,000+4\times10,000+2\times1,000+7\times1=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Perform the individual multiplications in the expression.
Step 2: Add the results of these multiplications.

Now, let's work through each step:
Step 1: Compute each multiplication term:
- $6 \times 100,000 = 600,000$
- $4 \times 10,000 = 40,000$
- $2 \times 1,000 = 2,000$
- $7 \times 1 = 7$

Step 2: Sum the results from Step 1:
$600,000 + 40,000 + 2,000 + 7 = 642,007$

Therefore, the solution to the equation is $642,007$ .

Final Answer

$642,007$

Key Points to Remember

Essential concepts to master this topic

Place Value: Each digit multiplies by its position value
Technique: Calculate 6×100,000 = 600,000, then add all terms
Check: Count digits in final answer: 642,007 has 6 digits ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include all place values
Don't skip the ones place or assume missing places equal zero = incomplete answer! Students often write 642,07 instead of 642,007. Always include every place value shown in the expanded form.

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 is there no tens or hundreds place in this problem?

Great observation! When a place value isn't shown in expanded form, it means that digit is zero. So this number has 0 tens and 0 hundreds, which is why we see 642,007.

Do I need to multiply 7×1 or can I just write 7?

You should write $7 \times 1 = 7$ to show you understand place value. The ones place has a value of 1, so every digit gets multiplied by its place value.

How do I add numbers with different place values?

Line up the place values! Write 600,000 + 40,000 + 2,000 + 7 in column form or just add from left to right: 600,000 + 40,000 = 640,000, then 640,000 + 2,000 = 642,000, finally 642,000 + 7 = 642,007.

What if I get confused by all the zeros?

Count carefully! 100,000 has 5 zeros, 10,000 has 4 zeros, 1,000 has 3 zeros. When you multiply, you keep the same number of zeros: 6×100,000 = 600,000 (still 5 zeros).

How can I check if 642,007 is correct?

Break it down by place value! 642,007 = 6 hundred-thousands + 4 ten-thousands + 2 thousands + 0 hundreds + 0 tens + 7 ones. This matches our original expanded form perfectly!

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