Choose the Correct Inequality Sign: 150,800 vs 158,000

Number Comparison with Large Values

Select the appropriate sign:

150,800158,000 150,800\Box158,000

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Select the appropriate sign:

150,800158,000 150,800\Box158,000

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify and compare the relevant place value digits of each number starting from the left.
  • Step 2: Decide on the appropriate inequality symbol based on comparison outcomes.

Now, let's work through each step:
Step 1: The problem gives us two numbers, 150,800 and 158,000. We will compare the digits from left to right.

- Start with the hundred thousand digits:
The digit in the hundred thousand place for both numbers is 1, which are equal. So, we continue to the next place.

- Next, compare the ten thousand digits:
150,800 has 5 in the ten thousand place and 158,000 has 5 as well. They are equal, so we move to the next digit.

- Now, compare the thousand digits:
150,800 has 0 in the thousand place, while 158,000 has 8.
Since 0 is less than 8, 150,800 is less than 158,000.

Therefore, the correct sign to use is <<, indicating that 150,800 is less than 158,000.

The solution to the problem is <<.

3

Final Answer

<

Key Points to Remember

Essential concepts to master this topic
  • Rule: Compare digits from left to right, starting with highest place value
  • Technique: When 150,800 vs 158,000, compare thousands place: 0 < 8
  • Check: Verify by counting: 150,800 is 7,200 less than 158,000 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing only the last digits or total digit count
    Don't just look at the ending 800 vs 000 or count that both have 6 digits = wrong comparison! The place value of each digit matters most. Always start comparing from the leftmost (highest place value) digit and work right.

Practice Quiz

Test your knowledge with interactive questions

Select the appropriate sign:

\( 24,909\Box24,990 \)

FAQ

Everything you need to know about this question

What if the first few digits are the same?

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Keep going right! When digits in the same place value are equal (like the 1 and 5 in both numbers), move to the next place value. The first different digit determines which number is larger.

How do I remember which way the inequality sign points?

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Think of the inequality sign as a hungry mouth - it always opens toward the larger number. So 150,800<158,000 150,800 < 158,000 shows the mouth opening to eat the bigger number!

Do commas in numbers affect the comparison?

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No! Commas are just for easier reading. Whether you write 150,800 or 150800, the value is exactly the same. Focus on the digit positions, not the commas.

What if one number has more digits than the other?

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The number with more digits is usually larger (like 1,000 > 999). But when both numbers have the same number of digits, compare place by place from left to right.

Can I subtract to compare the numbers?

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Yes! Subtracting 158,000150,800=7,200 158,000 - 150,800 = 7,200 gives a positive result, confirming that 158,000 is larger. But place-value comparison is usually faster.

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