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.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

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

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

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!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Natural numbers up to a million questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime