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

What number do the units shown below represent?

10,0001000111010100011

UnitsTensHundredsThousandsBeforeConversionAfterConversionTens ofThousands

Write the units 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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