Number Operations: Which Calculation Yields 200,060?

Place Value Decomposition with Large Numbers

Which is the correct exercise to attain the number 200,060?

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Step-by-step written solution

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1

Understand the problem

Which is the correct exercise to attain the number 200,060?

2

Step-by-step solution

1. Restate: The problem asks which mathematical exercise correctly represents the number 200,060 by breaking it down using the decimal structure. 2. Key Information: We need to reach the number 200,060. The number can be decomposed as parts of powers of ten. 3. Potential Approaches: Break down the number 200,060 according to the place values in the decimal system: hundreds of thousands, thousands, hundreds, tens, and ones. 4. Key Formulas: None required, just understanding of place value decomposition in the decimal system. 5. Appropriate Approach: Decompose 200,060 by identifying the parts they represent in terms of powers of ten. 6. Steps: - Start by identifying the highest place value in the number (hundreds of thousands). - Decompose into hundreds of thousands, then consider lower place values to complete the number. 7. Assumptions: None necessary beyond basic decimal structure understanding. 8. Complex Parts: Considering the separate components (parts of powers of ten) that add to 200,060. 9. Edge Cases: Not applicable. 10. Instructions: Analyze the correctness of given multiple-choice options. 11. Compare choices to determine which accurately adds up to 200,060. 12. Common Mistakes: Misidentifying place values, errors in addition. 13. Changes: Different values would directly change their respective impact on the addition to 200,060.

Let's solve this problem step by step:

  • Step 1: Identify the highest place value found in 200,060, which is hundreds of thousands.
  • Step 2: The number 200,060 can be broken down as follows:
    • It has 2 in the hundred thousand place, representing 2×100,000 2 \times 100,000 .
    • The tens place has 6, representing 6×10 6 \times 10 .
    • There are no thousands, hundreds, or ones to account for in the construction of 200,060.
  • Step 3: Check the calculations:
    • 2×100,000=200,000 2 \times 100,000 = 200,000
    • 6×10=60 6 \times 10 = 60
    • Add these results together: 200,000+60=200,060 200,000 + 60 = 200,060
  • Step 4: Evaluate the choices provided:
    • Choice 1 represents 1×100,000+2×10,000+6×10=120,060 1 \times 100,000 + 2 \times 10,000 + 6 \times 10 = 120,060 , which is incorrect.
    • Choice 2 represents 2×10,000+6×1,000=26,000 2 \times 10,000 + 6 \times 1,000 = 26,000 , which is incorrect.
    • Choice 3 represents 2×100,000+6×10=200,060 2 \times 100,000 + 6 \times 10 = 200,060 , which is correct.
    • Choice 4 represents 2×100,000+6×100=200,600 2 \times 100,000 + 6 \times 100 = 200,600 , which is incorrect.

Therefore, the decomposition exercise that correctly reaches the number 200,060 is:

2×100,000+6×10=200,060 2\times100,000+6\times10=200,060

3

Final Answer

2×100,000+6×10=200,060 2\times100,000+6\times10=200,060

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Each digit's position determines its value contribution
  • Technique: Break down 200,060 as 2×100,000+6×10 2 \times 100,000 + 6 \times 10
  • Check: Add components: 200,000 + 60 = 200,060 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing place values like tens vs hundreds
    Don't write 6×100 6 \times 100 for the 6 in the tens place = 200,600 instead of 200,060! This adds extra zeros where they don't belong. Always identify the exact position: 6 in tens place means 6×10 6 \times 10 .

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 know which place value each digit represents?

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Start from the right and count positions: ones, tens, hundreds, thousands, ten thousands, hundred thousands. The digit 6 in 200,060 is in the second position from right, so it's in the tens place.

Why are there zeros in 200,060 but not in the calculation?

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Zeros act as placeholders - they show that certain place values are empty. Since there are no thousands, hundreds, or ones in 200,060, we don't include them in our decomposition calculation.

What if I get confused about which multiplication to use?

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Write out the place value names under each digit:

  • 2 is in hundred thousands: 2×100,000 2 \times 100,000
  • 6 is in tens: 6×10 6 \times 10

How can I double-check my decomposition is correct?

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Add up all your components! If 2×100,000+6×10=200,000+60=200,060 2 \times 100,000 + 6 \times 10 = 200,000 + 60 = 200,060 , then your decomposition is correct.

Do I need to include place values with zero?

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No! Since 0×anything=0 0 \times \text{anything} = 0 , adding zero components doesn't change the total. Only include place values where the digit is not zero.

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