Number Identification: Finding the Expression Equal to 22,005

Place Value Decomposition with Multi-Digit Numbers

Choose the correct exercise that produces the number 22,005.

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Step-by-step written solution

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1

Understand the problem

Choose the correct exercise that produces the number 22,005.

2

Step-by-step solution

To solve this problem, we will decompose the number 22,005 using its place values and compare it with the provided answer choices.

First, let's break down the number 22,005:

  • The digit '2' in the ten-thousands place represents 2×10,000 2 \times 10,000 .
  • The digit '2' in the thousands place represents 2×1,000 2 \times 1,000 .
  • The digit '0' in the hundreds place represents 0×100 0 \times 100 .
  • The digit '0' in the tens place represents 0×10 0 \times 10 .
  • The digit '5' in the units place represents 5×1 5 \times 1 .

Combining these values, we have:

22,005=2×10,000+2×1,000+0×100+0×10+5×1 22,005 = 2 \times 10,000 + 2 \times 1,000 + 0 \times 100 + 0 \times 10 + 5 \times 1

Upon reviewing the provided choices, option 3 matches this decomposition exactly:

Choice 3: 22,005=2×10,000+2×1,000+0×100+0×10+5×1 22,005 = 2 \times 10,000 + 2 \times 1,000 + 0 \times 100 + 0 \times 10 + 5 \times 1

Therefore, the exercise that produces the number 22,005 is illustrated correctly in choice 3.

3

Final Answer

22,005=2×10,000+2×1,000+0×100+0×10+5×1 22,005=2\times10,000+2\times1,000+0\times100+0\times10+5\times1

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Each digit represents its value times its position
  • Technique: Break 22,005 into 2×10,000 + 2×1,000 + 0×100 + 0×10 + 5×1
  • Check: Add all components: 20,000 + 2,000 + 0 + 0 + 5 = 22,005 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing digit position with digit value
    Don't just look at the digits 2, 2, 0, 0, 5 and ignore their positions = wrong decomposition! The first 2 is in ten-thousands place (worth 20,000), not thousands place (worth 2,000). Always identify each digit's place value before writing the expression.

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

How do I remember which place value each position represents?

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Start from the right and work left: ones, tens, hundreds, thousands, ten-thousands. Each position is 10 times bigger than the one to its right!

What does it mean when a digit is 0?

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A zero digit means no value in that place. For example, 0×100 = 0, so the hundreds place contributes nothing to the total number.

Why do we write 0×10 instead of just leaving it out?

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Writing all place values shows the complete structure of the number, even when some positions are zero. It helps you see the pattern clearly!

How can I check if my decomposition is correct?

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Add up all the products! 2×10,000+2×1,000+0×100+0×10+5×1 2×10,000 + 2×1,000 + 0×100 + 0×10 + 5×1 should equal your original number.

What if I mixed up the place values?

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Double-check by counting positions from right to left. The rightmost digit is always the ones place, then tens, hundreds, and so on.

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