Calculate the Square Root of 68: Finding the Best Approximation

Rounding Numbers with Nearest Ten

68 ? 68\approx\text{ ?}

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Step-by-step written solution

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1

Understand the problem

68 ? 68\approx\text{ ?}

2

Step-by-step solution

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

  • Step 1: Identify the tens and units digits of the number 68.
  • Step 2: Use rounding rules to determine if we round up or down.
  • Step 3: Replace the units digit appropriately to find the rounded number.

Now, let's work through each step:
Step 1: The tens digit of 68 is 6, and the units digit is 8.
Step 2: Since the units digit (8) is 5 or greater, we round up the number 68.
Step 3: After rounding up, we replace the units digit with 0, resulting in the rounded number 70.

Therefore, the solution to the problem is 70 70 .

3

Final Answer

70 70

Key Points to Remember

Essential concepts to master this topic
  • Rounding Rule: Units digit 5 or greater rounds up to next ten
  • Technique: Check units digit: 68 has 8 ≥ 5, so round up
  • Check: Verify 70 is closer to 68 than 60: |68-70|=2 < |68-60|=8 ✓

Common Mistakes

Avoid these frequent errors
  • Rounding based on tens digit instead of units digit
    Don't look at the tens digit (6) to decide rounding direction = wrong answer 60! The tens digit tells you which ten you're near, but only the units digit determines if you round up or down. Always check the units digit: 8 ≥ 5 means round up to 70.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why do we round 68 to 70 instead of 60?

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The units digit determines rounding direction! Since 8 ≥ 5, we round up to the next ten. Think of it as 68 being closer to 70 (only 2 away) than to 60 (8 away).

What happens if the units digit is exactly 5?

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When the units digit is exactly 5, we always round up to the next ten. For example, 65 rounds up to 70, and 25 rounds up to 30.

How do I remember the rounding rule?

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Use this memory trick: "5 and above, give it a shove (up)!" If the units digit is 5, 6, 7, 8, or 9, always round up to the next ten.

What if I need to round to the nearest hundred instead?

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The same rule applies! Look at the tens digit instead of the units digit. If the tens digit is 5 or greater, round up to the next hundred.

Why does 68 become 70 and not just 7?

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We're rounding to the nearest ten, not the nearest single digit. The tens place value means we replace the units digit with 0, keeping the tens digit (or increasing it by 1 when rounding up).

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