Expanded Form Practice: Convert 10,654 into Place Value Notation

Place Value Decomposition with Five-Digit Numbers

Write the number 10,654 in its expanded form.

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Step-by-step written solution

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1

Understand the problem

Write the number 10,654 in its expanded form.

2

Step-by-step solution

To solve this problem, we will express the number 10,654 in its expanded form by considering each digit's position and multiplying it by its place value.

  • Step 1: Identify the digit and its place value.
    • The digit 1 is in the ten thousands place: 1×10,000 1 \times 10,000
    • The digit 0 is in the thousands place: 0×1,000 0 \times 1,000 (This will not affect the sum as it is zero)
    • The digit 6 is in the hundreds place: 6×100 6 \times 100
    • The digit 5 is in the tens place: 5×10 5 \times 10
    • The digit 4 is in the units place: 4×1 4 \times 1
  • Step 2: Write the expanded form by adding these products together.

Thus, the number can be expanded as follows:

10,654=1×10,000+0×1,000+6×100+5×10+4×1 10,654 = 1 \times 10,000 + 0 \times 1,000 + 6 \times 100 + 5 \times 10 + 4 \times 1

Simplifying the valid (non-zero) terms, we have:

10,654=1×10,000+6×100+5×10+4×1 10,654 = 1 \times 10,000 + 6 \times 100 + 5 \times 10 + 4 \times 1

Therefore, the expanded form of the number 10,654 is 1×10,000+6×100+5×10+4×1\boxed{1 \times 10,000 + 6 \times 100 + 5 \times 10 + 4 \times 1}, corresponding to choice 1.

3

Final Answer

10,654=1×10,000+6×100+5×10+4×1 10,654=1\times10,000+6\times100+5\times10+4\times1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Each digit multiplies by its position's place value
  • Technique: The 1 in 10,654 represents 1×10,000 1 \times 10,000
  • Check: Add all terms: 10,000 + 600 + 50 + 4 = 10,654 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing place value positions
    Don't write 1 as thousands instead of ten thousands = 1×1,000 1 \times 1,000 instead of 1×10,000 1 \times 10,000 ! This makes your total only 1,654 instead of 10,654. Always count place values carefully from right to left: ones, tens, hundreds, thousands, ten 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?

10,00010,00010,00010,00010101
UnitsTensHundredsThousandsBeforeConversionAfterConversionTens ofThousands

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

FAQ

Everything you need to know about this question

Why do we skip the zero in the thousands place?

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We can skip 0×1,000 0 \times 1,000 because zero times anything equals zero. Adding zero doesn't change the sum, so it's cleaner to leave it out of the expanded form.

How do I remember the place values?

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Start from the right and count: ones, tens, hundreds, thousands, ten thousands. Each place is 10 times larger than the place to its right!

What if I get confused about which digit goes where?

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Use a place value chart! Write the number above columns labeled with place values. The digit 1 in 10,654 sits in the ten thousands column.

Can I write the expanded form in a different order?

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Yes! You can write the terms in any order since we're adding them. However, it's conventional to write from largest place value to smallest for clarity.

How do I check if my expanded form is correct?

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Calculate each term separately, then add them all up: 10,000+0+600+50+4=10,654 10,000 + 0 + 600 + 50 + 4 = 10,654 . If you get the original number back, you're correct!

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