Square Root Problem: Find the Approximate Value of √7650

Q: How do I know which digit to look at when rounding?

Always look at the digit immediately to the right of the place you're rounding to. For thousands, check hundreds. For hundreds, check tens. This digit tells you whether to round up or down!

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

When the digit is 5 or greater, you always round up! In this problem, 6 is greater than 5, so we round $ 7650 $ up to $ 8000 $.

Q: Why isn't 7500 or 7600 the right answer?

These aren't rounded to the nearest thousand! The question asks for rounding to thousands place. 7500 is rounded to hundreds, and 7600 is rounded to tens. Only $ 8000 $ is a thousand.

Q: What does the ≈ symbol mean in this problem?

The ≈ symbol means "approximately equal to". It tells you that you're looking for the closest rounded value, not the exact number. Perfect for rounding problems like this one!

Rounding Numbers with Thousands Place Values

$7650\approx\text{ ?}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7650\approx\text{ ?}$

Step-by-step solution

To solve this problem, let's follow a systematic approach:

Step 1: Identify the number to be rounded, which is $7650$ .
Step 2: Determine whether we're rounding to the nearest 1,000. Given the problem and available choices, this seems the most logical interpretation.
Step 3: Look at the hundreds digit of 7650. It is 6, since 7650 can be broken down into 7 (thousands), 6 (hundreds), 5 (tens), and 0 (units).
Step 4: Since the hundreds digit is 6, which is 5 or greater, we round up to the next highest thousand.

Thus, rounding 7650 to the nearest 1,000 gives us $8000$ .

Final Answer

$8000$

Key Points to Remember

Essential concepts to master this topic

Rule: Look at the digit immediately after your target place
Technique: For 7650 to nearest thousand, check hundreds digit: 6 ≥ 5
Check: Verify 8000 is closer to 7650 than 7000 by 650 units ✓

Common Mistakes

Avoid these frequent errors

Looking at the wrong digit when rounding
Don't look at the tens digit (5) when rounding to thousands = wrong answer 7000! The tens digit doesn't determine thousands place rounding. Always look at the hundreds digit (6) which tells us to round up to 8000.

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 digit to look at when rounding?

Always look at the digit immediately to the right of the place you're rounding to. For thousands, check hundreds. For hundreds, check tens. This digit tells you whether to round up or down!

What if the digit I'm checking is exactly 5?

When the digit is 5 or greater, you always round up! In this problem, 6 is greater than 5, so we round $7650$ up to $8000$ .

Why isn't 7500 or 7600 the right answer?

These aren't rounded to the nearest thousand! The question asks for rounding to thousands place. 7500 is rounded to hundreds, and 7600 is rounded to tens. Only $8000$ is a thousand.

How can I double-check my rounding?

Find the distance from your original number to each possible answer. $7650$ is 650 away from $8000$ but 650 away from $7000$ too. Since we round up when the digit is ≥5, 8000 is correct!

What does the ≈ symbol mean in this problem?

The ≈ symbol means "approximately equal to". It tells you that you're looking for the closest rounded value, not the exact number. Perfect for rounding problems like this one!

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