Select the Correct Approximation of 33,184

Q: Why do we round 33,184 down to 33,180 instead of up to 33,190?

Because the ones digit is 4, which is less than 5. The rounding rule says: if the digit is 0-4, round down; if it's 5-9, round up. Since 4

Q: What does 'rounding to the nearest ten' actually mean?

It means finding the multiple of 10 that's closest to your number. For 33,184, the closest tens are 33,180 and 33,190. Since 33,184 is only 4 away from 33,180 but 6 away from 33,190, we choose 33,180.

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

Always look at the digit one place to the right of where you're rounding to. Rounding to tens? Look at the ones digit. Rounding to hundreds? Look at the tens digit.

Q: What if the ones digit was exactly 5?

If the ones digit is 5, we round up by convention. So 33,185 would round up to 33,190, not down to 33,180.

Q: Can I just estimate without using the rounding rule?

Not recommended! While 33,184 looks close to 33,200, the systematic rounding rule ensures accuracy. Mental estimation can lead to errors, especially with larger numbers.

Rounding Numbers with Tens Place Precision

Choose the correct answer:

$33,184\approx\text{ ?}$

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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:

$33,184\approx\text{ ?}$

Step-by-step solution

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

Step 1: Identify the digit in the ones place.
Step 2: Apply the rounding rule to determine rounding direction (up or down).
Step 3: Round the number and match it to the choices provided.

Now, let's work through each step:
Step 1: The number is 33,184, and the digit in the ones place is 4.
Step 2: According to the rounding rules, since 4 is less than 5, we round down. Thus, the tens place remains unchanged while the ones digit becomes zero.
Step 3: As a result, 33,184 rounds to $33,180$ .

Therefore, the solution to the problem is $33,180$ .

Final Answer

$33,180$

Key Points to Remember

Essential concepts to master this topic

Rule: Look at the ones digit to determine rounding direction
Technique: Since 4 < 5, round down: 33,184 becomes 33,180
Check: Verify 33,180 is closest to 33,184 among all choices ✓

Common Mistakes

Avoid these frequent errors

Looking at the wrong digit for rounding
Don't look at the tens digit (8) or hundreds digit (1) when rounding to tens = wrong direction! You'll round 33,184 to 33,190 instead of 33,180. Always look at the ones digit (4) to determine whether to round up or down.

Practice Quiz

Test your knowledge with interactive questions

Choose the right answer:

$12,346\approx\text{ ?}$

FAQ

Everything you need to know about this question

Why do we round 33,184 down to 33,180 instead of up to 33,190?

Because the ones digit is 4, which is less than 5. The rounding rule says: if the digit is 0-4, round down; if it's 5-9, round up. Since 4 < 5, we round down!

What does 'rounding to the nearest ten' actually mean?

It means finding the multiple of 10 that's closest to your number. For 33,184, the closest tens are 33,180 and 33,190. Since 33,184 is only 4 away from 33,180 but 6 away from 33,190, we choose 33,180.

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

Always look at the digit one place to the right of where you're rounding to. Rounding to tens? Look at the ones digit. Rounding to hundreds? Look at the tens digit.

What if the ones digit was exactly 5?

If the ones digit is 5, we round up by convention. So 33,185 would round up to 33,190, not down to 33,180.

Can I just estimate without using the rounding rule?

Not recommended! While 33,184 looks close to 33,200, the systematic rounding rule ensures accuracy. Mental estimation can lead to errors, especially with larger numbers.

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