Approximating 2567: Find the Nearest Value

Q: How do I know which place value to round to?

Look at the answer choices to see what place value they represent. Here, choices like 2500, 2600 show we're rounding to the nearest hundred, not thousand.

Q: What if the digit I'm looking at is exactly 5?

When the deciding digit is exactly 5, always round up. For example, 2550 would round up to 2600, not down to 2500.

Q: Why is 2600 better than 2500 for approximating 2567?

Check the distances: $ |2567 - 2600| = 33 $ versus $ |2567 - 2500| = 67 $. Since 33 2600 is closer.

Q: Can I round in steps, like first to tens then hundreds?

No! Always round directly to the target place value. Rounding in steps can give wrong answers because each step introduces error that compounds.

Q: What does the ≈ symbol mean?

The symbol ≈ means "approximately equal to". It tells us we're looking for the closest value, not an exact answer.

Number Rounding with Nearest Hundreds

$2567\approx\text{ ?}$

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Step-by-step written solution

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Understand the problem

$2567\approx\text{ ?}$

Step-by-step solution

To solve this problem, we'll round the number 2567 to the nearest hundred:

Step 1: Identify the relevant digits: For 2567, the hundreds digit is 5, and the tens digit is 6.
Step 2: Determine the rounding rule: Since the tens digit (6) is 5 or greater, we will round up.
Step 3: Apply the rounding: Adding one to the hundreds digit, 2567 rounds up to 2600.

Therefore, rounding 2567 to the nearest hundred places gives us the solution: $2600$ .

Final Answer

$2600$

Key Points to Remember

Essential concepts to master this topic

Rounding Rule: Look at tens digit to determine direction
Technique: Since tens digit 6 ≥ 5, round up from 2567 to 2600
Check: Verify 2567 is closer to 2600 than 2500: |2567-2600| = 33 ✓

Common Mistakes

Avoid these frequent errors

Rounding to wrong place value
Don't round 2567 to the nearest thousand (3000) when asked for approximation! This creates a much larger error of 433 instead of 33. Always identify the appropriate place value from context or given options.

Practice Quiz

Test your knowledge with interactive questions

$52\approx\text{ ?}$

FAQ

Everything you need to know about this question

How do I know which place value to round to?

Look at the answer choices to see what place value they represent. Here, choices like 2500, 2600 show we're rounding to the nearest hundred, not thousand.

What if the digit I'm looking at is exactly 5?

When the deciding digit is exactly 5, always round up. For example, 2550 would round up to 2600, not down to 2500.

Why is 2600 better than 2500 for approximating 2567?

Check the distances: $|2567 - 2600| = 33$ versus $|2567 - 2500| = 67$ . Since 33 < 67, 2600 is closer.

Can I round in steps, like first to tens then hundreds?

No! Always round directly to the target place value. Rounding in steps can give wrong answers because each step introduces error that compounds.

What does the ≈ symbol mean?

The symbol ≈ means "approximately equal to". It tells us we're looking for the closest value, not an exact answer.

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