Approximating 5,617: Finding the Nearest Round Number

Q: Why do I look at the hundreds digit when rounding to thousands?

The hundreds digit tells you which thousand is closer! If it's 5 or more, the number is closer to the higher thousand. If it's 4 or less, it's closer to the lower thousand.

Q: What if the hundreds digit is exactly 5?

When the hundreds digit is exactly 5, we follow the rule to round up. So 5,500 would round up to 6,000, not down to 5,000.

Q: How can I double-check my rounding?

Calculate the distance to both options! For 5,617: distance to 5,000 is 617, distance to 6,000 is 383. Since 383

Q: What does the ≈ symbol mean?

The symbol $ \approx $ means "approximately equal to" or "about equal to". It shows that 5,617 is close to but not exactly 6,000.

Q: Do I need to change all the other digits to zero?

Yes! When rounding to the nearest thousand, all digits to the right of the thousands place become zero. So 5,617 becomes 6,000.

Q: What if I'm rounding to nearest hundred instead?

Then you'd look at the tens digit instead! For 5,617, the tens digit is 1, so you'd round down to 5,600 when rounding to the nearest hundred.

Rounding Numbers with Nearest Thousands

Choose the correct answer:

$5,617\approx$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the correct answer:

$5,617\approx$

Step-by-step solution

To solve this problem, we'll round the number $5,617$ to the nearest multiple of $1,000$ using the standard rounding rules.

Here's how we can do it:

First, we need to look at the hundreds digit of $5,617$ . This digit is $6$ .
According to the rounding rule: - If the hundreds digit is $5$ or greater, we round up. - If the hundreds digit is $4$ or less, we round down.
Since the hundreds digit here is $6$ , which is greater than $5$ , we will round $5,617$ up to the nearest $1,000$ .

This means $5,617$ rounds to $6,000$ .

Therefore, the solution to the problem is $6,000$ .

Final Answer

$6,000$

Key Points to Remember

Essential concepts to master this topic

Rounding Rule: Look at hundreds digit to determine direction
Technique: 5,617 has 6 in hundreds place, so round up
Check: 5,617 is closer to 6,000 than 5,000 by 383 units ✓

Common Mistakes

Avoid these frequent errors

Looking at the wrong digit for rounding
Don't look at the tens digit (1) or ones digit (7) when rounding to nearest thousand = wrong answer! These digits don't determine thousand-place rounding. Always look at the hundreds digit to decide whether to round up or down.

Practice Quiz

Test your knowledge with interactive questions

Choose the right answer:

$39,133\approx\text{ ?}$

FAQ

Everything you need to know about this question

Why do I look at the hundreds digit when rounding to thousands?

The hundreds digit tells you which thousand is closer! If it's 5 or more, the number is closer to the higher thousand. If it's 4 or less, it's closer to the lower thousand.

What if the hundreds digit is exactly 5?

When the hundreds digit is exactly 5, we follow the rule to round up. So 5,500 would round up to 6,000, not down to 5,000.

How can I double-check my rounding?

Calculate the distance to both options! For 5,617: distance to 5,000 is 617, distance to 6,000 is 383. Since 383 < 617, the answer is 6,000.

What does the ≈ symbol mean?

The symbol $\approx$ means "approximately equal to" or "about equal to". It shows that 5,617 is close to but not exactly 6,000.

Do I need to change all the other digits to zero?

Yes! When rounding to the nearest thousand, all digits to the right of the thousands place become zero. So 5,617 becomes 6,000.

What if I'm rounding to nearest hundred instead?

Then you'd look at the tens digit instead! For 5,617, the tens digit is 1, so you'd round down to 5,600 when rounding to the nearest hundred.

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