Expanded Form: Converting 58,570 to Place Value Notation

Q: What if there's a zero in the middle of the number?

Include the zero! Write it as 0 × (place value). For 58,570, the ones place is $ 0 \times 1 $. Even though it equals 0, it shows you understand place value completely.

Q: Do I always have to write every place value?

Yes, for expanded form! Even if a digit is 0, include it in your answer. This shows you recognize every position in the number and understand place value thoroughly.

Q: How do I remember which place value is which?

Start from the right side (ones place) and work left: ones, tens, hundreds, thousands, ten-thousands. Each position is 10 times bigger than the one before it.

Q: Can I write the expanded form in a different order?

While addition is commutative, it's best practice to write from largest to smallest place value. This matches how we read numbers and makes it easier to check your work.

Q: What's the difference between expanded form and standard form?

Standard form is the regular way we write numbers (58,570). Expanded form breaks it down to show each digit's place value: $ 5 \times 10,000 + 8 \times 1,000 + 5 \times 100 + 7 \times 10 + 0 \times 1 $.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Write 58,570 in its expanded form.

2

Step-by-step solution

To solve the problem of expressing 58,570 in expanded form, follow these steps:

Identify the Place Value of Each Digit:
- 5 is in the ten-thousands place.
- 8 is in the thousands place.
- 5 is in the hundreds place.
- 7 is in the tens place.
- 0 is in the ones place.
Multiply Each Digit by its Place Value:
- The digit 5 (ten-thousands) represents $5 \times 10,000$ .
- The digit 8 (thousands) represents $8 \times 1,000$ .
- The digit 5 (hundreds) represents $5 \times 100$ .
- The digit 7 (tens) represents $7 \times 10$ .
- The digit 0 (ones) represents $0 \times 1$ .
Express the Number as a Sum of these Terms:
Combine these into an expression: $5 \times 10,000 + 8 \times 1,000 + 5 \times 100 + 7 \times 10 + 0 \times 1$ .

Therefore, the expanded form of 58,570 is $58,570 = 5 \times 10,000 + 8 \times 1,000 + 5 \times 100 + 7 \times 10 + 0 \times 1$ .

3

Final Answer

$58,570=5\times10,000+8\times1,000+5\times100+7\times10+0\times1$

Key Points to Remember

Essential concepts to master this topic

Digit Position: Each position represents a specific power of ten
Technique: Write $5 \times 10,000 + 8 \times 1,000$ for first two digits
Check: Add all products: 50,000 + 8,000 + 500 + 70 + 0 = 58,570 ✓

Common Mistakes

Avoid these frequent errors

Mixing up digit positions or place values
Don't write the digits in wrong positions like putting 5 in thousands place instead of ten-thousands = completely wrong number! This changes the entire value. Always identify each digit's exact position from right to left: ones, tens, hundreds, thousands, ten-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

What if there's a zero in the middle of the number?

+

Include the zero! Write it as 0 × (place value). For 58,570, the ones place is $0 \times 1$ . Even though it equals 0, it shows you understand place value completely.

Do I always have to write every place value?

+

Yes, for expanded form! Even if a digit is 0, include it in your answer. This shows you recognize every position in the number and understand place value thoroughly.

How do I remember which place value is which?

+

Start from the right side (ones place) and work left: ones, tens, hundreds, thousands, ten-thousands. Each position is 10 times bigger than the one before it.

Can I write the expanded form in a different order?

+

While addition is commutative, it's best practice to write from largest to smallest place value. This matches how we read numbers and makes it easier to check your work.

What's the difference between expanded form and standard form?

+

Standard form is the regular way we write numbers (58,570). Expanded form breaks it down to show each digit's place value: $5 \times 10,000 + 8 \times 1,000 + 5 \times 100 + 7 \times 10 + 0 \times 1$ .

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Expanded Form: Converting 58,570 to Place Value Notation

Place Value with Five-Digit Decomposition

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Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What if there's a zero in the middle of the number?

Do I always have to write every place value?

How do I remember which place value is which?

Can I write the expanded form in a different order?

What's the difference between expanded form and standard form?

🌟 Unlock Your Math Potential

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