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

Follow each step carefully to understand the complete solution
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

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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

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

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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