Number Decomposition: Breaking Down 701,005 into Place Values

Q: How do I remember the place value names for big numbers?

Start from the right and count: ones, tens, hundreds (first group), then thousands, ten-thousands, hundred-thousands (second group). The pattern repeats every three places!

Q: What do I do with the zeros in 701,005?

Zeros mean no value in that place! So $ 0 \times 10,000 = 0 $ and $ 0 \times 100 = 0 $. Since they equal zero, you can skip them in your decomposition.

Q: Why don't we write all the zero terms?

Adding zero doesn't change the sum! Writing $ 7 \times 100,000 + 0 \times 10,000 + 1 \times 1,000 + 0 \times 100 + 0 \times 10 + 5 \times 1 $ is correct but unnecessarily long.

Q: What's the difference between 1,000 and 10,000?

1,000 is one thousand (thousands place), while 10,000 is ten thousand (ten-thousands place). Count the zeros: 1,000 has 3 zeros, 10,000 has 4 zeros!

Place Value Decomposition with Large Numbers

Choose the correct decomposition of the number 701,005.

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Step-by-step written solution

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Understand the problem

Choose the correct decomposition of the number 701,005.

Step-by-step solution

To solve this problem, we need to decompose the number 701,005 based on its digit values and their respective place values.

Let's break down the number 701,005:

There is a 7 in the hundred-thousands place: $7 \times 100,000$
There is a 0 in the ten-thousands place: $0 \times 10,000$ (this contributes nothing to the sum, so it can be ignored)
There is a 1 in the thousands place: $1 \times 1,000$
There is a 0 in the hundreds place: $0 \times 100$ (this contributes nothing)
There is a 0 in the tens place: $0 \times 10$ (this contributes nothing)
There is a 5 in the units place: $5 \times 1$

Now, let's put these together to express 701,005:

$701,005 = 7 \times 100,000 + 1 \times 1,000 + 5 \times 1$

Upon comparison with the given options, choice 1 correctly presents this decomposition:

$7\times100,000+1\times1,000+5\times1=701,005$

Therefore, the correct decomposition of 701,005 is given by choice 1.

Final Answer

$7\times100,000+1\times1,000+5\times1=701,005$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each digit's position determines its multiplicative value
Technique: Work left to right: 7 in hundred-thousands = $7 \times 100,000$
Check: Add all terms: 700,000 + 1,000 + 5 = 701,005 ✓

Common Mistakes

Avoid these frequent errors

Misidentifying place values in large numbers
Don't confuse thousands with ten-thousands positions = wrong powers of 10! Students often miscount places when numbers have zeros, leading to incorrect decompositions like $7 \times 1,000$ instead of $7 \times 100,000$ . Always count place values carefully from right to left: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands.

Practice Quiz

Test your knowledge with interactive questions

What number do the units shown below represent?

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

FAQ

Everything you need to know about this question

How do I remember the place value names for big numbers?

Start from the right and count: ones, tens, hundreds (first group), then thousands, ten-thousands, hundred-thousands (second group). The pattern repeats every three places!

What do I do with the zeros in 701,005?

Zeros mean no value in that place! So $0 \times 10,000 = 0$ and $0 \times 100 = 0$ . Since they equal zero, you can skip them in your decomposition.

Why don't we write all the zero terms?

Adding zero doesn't change the sum! Writing $7 \times 100,000 + 0 \times 10,000 + 1 \times 1,000 + 0 \times 100 + 0 \times 10 + 5 \times 1$ is correct but unnecessarily long.

How can I check if my decomposition is right?

Calculate each term separately, then add them up! For example: $7 \times 100,000 = 700,000$ , $1 \times 1,000 = 1,000$ , $5 \times 1 = 5$ . Then 700,000 + 1,000 + 5 = 701,005 ✓

What's the difference between 1,000 and 10,000?

1,000 is one thousand (thousands place), while 10,000 is ten thousand (ten-thousands place). Count the zeros: 1,000 has 3 zeros, 10,000 has 4 zeros!

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