Approximation Challenge: Estimating 431 to the Nearest Ten or Hundred

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

When rounding to the nearest hundred, look at the tens digit (the middle digit in a 3-digit number). If it's 5 or more, round up. If it's less than 5, round down.

Q: What if the tens digit is exactly 5?

When the tens digit is exactly 5, we round up to the next hundred. For example, 451 would round up to 500, and 350 would round up to 400.

Q: How can I double-check my rounding?

Find the distance from your number to both hundreds: $ |431 - 400| = 31 $ and $ |431 - 500| = 69 $The smaller distance shows the correct answer!

Q: Do I always round 431 to 400?

Only when rounding to the nearest hundred! For nearest ten, 431 becomes 430. For nearest thousand, it becomes 0. Always check what place value you're rounding to.

Rounding Numbers with Hundreds Place Focus

$431\approx\text{ ?}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$431\approx\text{ ?}$

Step-by-step solution

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

Step 1: Identify the tens digit of the number 431.
Step 2: Apply the rounding rule to the nearest hundred.
Step 3: Compare with the given choices to select the correct answer.

Now, let's work through each step:
Step 1: The number is 431, and the tens digit is 3 (from the 31 portion).
Step 2: According to rounding rules, since the tens digit (3) is less than 5, we round down. Thus, 431 rounded to the nearest hundred is 400.
Step 3: The choices provided are 500, 400, 440, and 430. The rounded result, 400, matches choice 2.

Therefore, the correct approximation of 431, rounding to the nearest hundred, is $400$ .

Final Answer

$400$

Key Points to Remember

Essential concepts to master this topic

Rounding Rule: Tens digit less than 5 means round down
Technique: Look at tens digit 3 in 431, round to 400
Check: Distance from 431 to 400 is 31, closer than to 500 ✓

Common Mistakes

Avoid these frequent errors

Rounding to the nearest ten instead of hundred
Don't look at just the ones digit 1 and round 431 to 430! This gives you the nearest ten, not hundred. The problem asks for approximation to the nearest hundred, so always examine the tens digit to determine hundreds place rounding.

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?

When rounding to the nearest hundred, look at the tens digit (the middle digit in a 3-digit number). If it's 5 or more, round up. If it's less than 5, round down.

Why isn't 430 the right answer if it's closest to 431?

Great observation! While 430 is numerically closest, the question asks for rounding to the nearest hundred, not ten. We must choose between 400 and 500, and 431 is closer to 400.

What if the tens digit is exactly 5?

When the tens digit is exactly 5, we round up to the next hundred. For example, 451 would round up to 500, and 350 would round up to 400.

How can I double-check my rounding?

Find the distance from your number to both hundreds: $|431 - 400| = 31$ and $|431 - 500| = 69$
The smaller distance shows the correct answer!

Do I always round 431 to 400?

Only when rounding to the nearest hundred! For nearest ten, 431 becomes 430. For nearest thousand, it becomes 0. Always check what place value you're rounding to.

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