Number Decomposition: Breaking Down 352,001 into Place Values

Place Value Decomposition with Large Numbers

Choose the correct decomposition of the number 352,001.

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Step-by-step written solution

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1

Understand the problem

Choose the correct decomposition of the number 352,001.

2

Step-by-step solution

To solve this problem, we need to decompose the number 352,001 into its decimal place values.

Let's break this down:

  • Hundred Thousands Place: The digit '3' is in the hundred thousands place.
    The value is 3×100,000=300,000 3 \times 100,000 = 300,000 .
  • Ten Thousands Place: The digit '5' is in the ten thousands place.
    The value is 5×10,000=50,000 5 \times 10,000 = 50,000 .
  • Thousands Place: The digit '2' is in the thousands place.
    The value is 2×1,000=2,000 2 \times 1,000 = 2,000 .
  • Hundreds Place: There is no digit in the hundreds place, so the value is 0×100=0 0 \times 100 = 0 .
  • Tens Place: There is no digit in the tens place, so the value is 0×10=0 0 \times 10 = 0 .
  • Units Place: The digit '1' is in the units place.
    The value is 1×1=1 1 \times 1 = 1 .

Now, we add these values together to verify decomposition:
300,000+50,000+2,000+0+0+1=352,001 300,000 + 50,000 + 2,000 + 0 + 0 + 1 = 352,001 .

Hence, the correct decomposition of the number 352,001 is:

3×100,000+5×10,000+2×1,000+1×1=352,001 3 \times 100,000 + 5 \times 10,000 + 2 \times 1,000 + 1 \times 1 = 352,001 .

We compare this to the choices provided and see that it matches .

Therefore, the solution to the problem is 3×100,000+5×10,000+2×1,000+1×1=352,001 3 \times 100,000 + 5 \times 10,000 + 2 \times 1,000 + 1 \times 1 = 352,001 .

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Final Answer

3×100,000+5×10,000+2×1,000+1×1=352,001 3\times100,000+5\times10,000+2\times1,000+1\times1=352,001

Key Points to Remember

Essential concepts to master this topic
  • Rule: Each digit's position determines its place value power
  • Technique: Write 3×100,000=300,000 3 \times 100,000 = 300,000 for hundreds place
  • Check: Add all parts: 300,000 + 50,000 + 2,000 + 1 = 352,001 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting zero place holders
    Don't write 1 × 100 for the units digit in 352,001 = wrong place value! The zeros in the middle don't disappear - they show empty hundreds and tens places. Always identify each digit's exact position from right to left.

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 don't we include the zeros in 352,001?

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We do account for zeros - they just equal zero! The zeros mean there are no hundreds and no tens, so we get 0×100=0 0 \times 100 = 0 and 0×10=0 0 \times 10 = 0 .

How do I remember which place is which?

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Start from the right and count: ones, tens, hundreds, thousands, ten thousands, hundred thousands. Each place is 10 times bigger than the one before it!

What if I mix up the place values?

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Write the number with place value labels above each digit first. For 352,001: hundred thousands (3), ten thousands (5), thousands (2), hundreds (0), tens (0), ones (1).

Why does 1 × 1 equal 1 in the units place?

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The units place (or ones place) has a value of 1. So the digit 1 in that position means 1×1=1 1 \times 1 = 1 , not 1 × 10 or 1 × 100.

Can I write the decomposition in a different order?

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Yes! You can write the terms in any order since addition is commutative. But it's clearest to go from largest to smallest place value for easy checking.

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