Approximate 870: Understanding Nearest Value Techniques

Q: Why do we look at the tens digit instead of the units digit?

When rounding to the nearest hundred, you look at the digit one place to the right of what you're rounding to. Since hundreds place needs the tens digit to decide, we check if the tens digit is ≥5.

Q: What if the tens digit is exactly 5?

When the tens digit equals 5, we follow the same rule: round up! So 850 would round up to 900, not down to 800.

Q: How do I know which hundred 870 is closer to?

Compare distances: 870 to 800 = 70 units away, but 870 to 900 = only 30 units away. Since 30 , we choose 900 as our answer.

Q: What if all the answer choices seem wrong?

Double-check your rounding rules! Remember: tens digit 5 or higher means round up, 4 or lower means round down. For 870, the tens digit 7 definitely means round up to 900.

Q: Is there a difference between ≈ and = symbols?

Yes! The ≈ symbol means "approximately equal to" while = means exactly equal. Since 870 ≈ 900 but 870 ≠ 900, we use the approximation symbol.

Rounding Numbers with Nearest Hundred Approximation

$870\approx\text{ ?}$

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Step-by-step written solution

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Understand the problem

$870\approx\text{ ?}$

Step-by-step solution

To solve this problem, we will round the number $870$ to the nearest hundred. Let's follow these steps:

Step 1: Identify the tens digit of $870$ . Here, the tens digit is $7$ .
Step 2: Apply the rounding rule to the hundreds place. Since the tens digit $7$ is greater than or equal to $5$ , we will round up.
Step 3: The hundreds digit will be increased by $1$ , rounding $870$ up to the next hundred.

After rounding, $870$ becomes $900$ .

Thus, the correct answer to the problem is $900$ , corresponding to choice id .

Final Answer

$900$

Key Points to Remember

Essential concepts to master this topic

Rounding Rule: Look at tens digit to decide up or down
Technique: Since 7 ≥ 5, round 870 up to 900
Check: Verify 870 is closer to 900 than 800: |870-900|=30 < 70 ✓

Common Mistakes

Avoid these frequent errors

Looking at the wrong digit when rounding
Don't look at the units digit (0) when rounding to hundreds = wrong direction! The units digit doesn't determine rounding to hundreds place. Always look at the tens digit (7 in 870) to decide whether to round up or down.

Practice Quiz

Test your knowledge with interactive questions

$52\approx\text{ ?}$

FAQ

Everything you need to know about this question

Why do we look at the tens digit instead of the units digit?

When rounding to the nearest hundred, you look at the digit one place to the right of what you're rounding to. Since hundreds place needs the tens digit to decide, we check if the tens digit is ≥5.

What if the tens digit is exactly 5?

When the tens digit equals 5, we follow the same rule: round up! So 850 would round up to 900, not down to 800.

How do I know which hundred 870 is closer to?

Compare distances: 870 to 800 = 70 units away, but 870 to 900 = only 30 units away. Since 30 < 70, we choose 900 as our answer.

What if all the answer choices seem wrong?

Double-check your rounding rules! Remember: tens digit 5 or higher means round up, 4 or lower means round down. For 870, the tens digit 7 definitely means round up to 900.

Is there a difference between ≈ and = symbols?

Yes! The ≈ symbol means "approximately equal to" while = means exactly equal. Since 870 ≈ 900 but 870 ≠ 900, we use the approximation symbol.

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