Calculate the Square Root: Finding the Approximation of √6430

Q: Why do we look at the hundreds digit to round to thousands?

The hundreds digit tells us which thousand we're closer to. In 6430, the 4 in the hundreds place means we're closer to 6000 than 7000. It's like asking: are we more than halfway to the next thousand?

Q: What if the hundreds digit is exactly 5?

When the hundreds digit is 5 or greater, we round UP to the next thousand. For example, 6530 would round up to 7000 because 5 ≥ 5.

Q: Do I need to look at the tens and ones digits too?

No! When rounding to thousands, only the hundreds digit matters. The tens and ones digits (30 in this case) don't affect whether we round up or down to the nearest thousand.

Q: How can I remember which direction to round?

Use this simple rule: "5 and above, give it a shove (up)" and "4 and below, let it go (down)". Since our hundreds digit is 4, we round down!

Q: Why isn't 6500 the correct answer?

6500 would be rounding to the nearest hundred, not thousand! We need the closest thousand, which are 6000 and 7000. Since 6430 is only 430 away from 6000 but 570 away from 7000, 6000 is correct.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$6430\approx\text{ ?}$

2

Step-by-step solution

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

Step 1: Identify the hundreds digit in the number 6430.
Step 2: Apply the rounding rule for determining the nearest thousand.
Step 3: Conclude with the rounded number based on the calculated rule.

Now, let's work through each step:
Step 1: The given number is $6430$ . The hundreds digit in this number is $4$ (from left-to-right, the number reads as 6000 + 400 + 30).
Step 2: According to the rounding rule, if the hundreds digit is less than 5, we round down. Since $4$ is less than $5$ , we will round 6430 down to 6000.
Step 3: Based on this calculation, the number 6430 rounded to the nearest thousand is 6000.

Therefore, the solution to the problem is $6000$ .

3

Final Answer

$6000$

Key Points to Remember

Essential concepts to master this topic

Rounding Rule: Look at hundreds digit to round to nearest thousand
Technique: Since 4 < 5 in 6430, round down to 6000
Check: Verify 6430 is closer to 6000 than 7000: distance is 430 vs 570 ✓

Common Mistakes

Avoid these frequent errors

Looking at the wrong digit for rounding
Don't look at the tens or ones digit when rounding to thousands = wrong answer every time! Students often focus on the last digit instead of the hundreds place. Always identify the hundreds digit (third from right) to determine rounding direction.

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 hundreds digit to round to thousands?

+

The hundreds digit tells us which thousand we're closer to. In 6430, the 4 in the hundreds place means we're closer to 6000 than 7000. It's like asking: are we more than halfway to the next thousand?

What if the hundreds digit is exactly 5?

+

When the hundreds digit is 5 or greater, we round UP to the next thousand. For example, 6530 would round up to 7000 because 5 ≥ 5.

Do I need to look at the tens and ones digits too?

+

No! When rounding to thousands, only the hundreds digit matters. The tens and ones digits (30 in this case) don't affect whether we round up or down to the nearest thousand.

How can I remember which direction to round?

+

Use this simple rule: "5 and above, give it a shove (up)" and "4 and below, let it go (down)". Since our hundreds digit is 4, we round down!

Why isn't 6500 the correct answer?

+

6500 would be rounding to the nearest hundred, not thousand! We need the closest thousand, which are 6000 and 7000. Since 6430 is only 430 away from 6000 but 570 away from 7000, 6000 is correct.

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