Calculate the Square Root: Finding the Approximate Value of √465

Rounding Numbers with Units Digit Five

465 ? 465\approx\text{ ?}

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Step-by-step written solution

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1

Understand the problem

465 ? 465\approx\text{ ?}

2

Step-by-step solution

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

  • Step 1: Identify the tens and units digits in 465.
  • Step 2: Apply the rounding rule for the nearest ten.
  • Step 3: Determine the rounded value based on the rule.

Now, let's work through each step:
Step 1: The number 465 has 6 in the tens place and 5 in the units place.

Step 2: To round to the nearest ten, we look at the units digit (5). According to rounding rules, if the digit is 5 or more, we round up.

Step 3: Since the units digit of 465 is 5, we round 460 up to 470.

Therefore, the rounded value of 465 to the nearest ten is 470 470 .

3

Final Answer

470 470

Key Points to Remember

Essential concepts to master this topic
  • Rule: When units digit is 5 or greater, round up to next ten
  • Technique: Look at units place: 465 has 5, so round 460 up to 470
  • Check: Verify 470 is closer to 465 than 460: |470-465| = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Rounding down when units digit is 5
    Don't round 465 down to 460 just because it seems closer! The standard rounding rule states that 5 rounds UP, not down. This gives you 460 instead of the correct 470. Always round up when the units digit is exactly 5.

Practice Quiz

Test your knowledge with interactive questions

\( 52\approx\text{ ?} \)

FAQ

Everything you need to know about this question

Why do we round 5 up instead of down?

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The standard rounding rule is that 5 or greater rounds up. This creates consistency in mathematics - we always know what to do with 5! Some people think 5 is 'in the middle' but the rule keeps everything uniform.

What if the number ends in 4?

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Numbers ending in 0, 1, 2, 3, or 4 round down to the nearest ten. For example, 464 would round down to 460 because 4 is less than 5.

How do I remember which direction to round?

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Think of it as a split at 5: digits 0-4 go down, digits 5-9 go up. You can also remember '5 and above, give it a shove (up)'!

What does 'approximate' mean in math?

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Approximate means 'close to but not exactly'. When we write 465470 465 \approx 470 , we're saying 465 is approximately equal to 470 - close enough for many purposes!

Can I round to the nearest hundred instead?

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Yes! To round 465 to the nearest hundred, look at the tens digit (6). Since 6 ≥ 5, round up: 465 rounds to 500. Different rounding gives different approximations.

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