Calculate the Square Root of 1367: Finding the Exact Approximation

Q: Why do I look at the tens digit and not the units digit?

When rounding to the nearest hundred, the tens digit tells you which hundred is closer. The units digit only matters when rounding to the nearest ten!

Q: What happens if the tens digit is exactly 5?

When the tens digit is 5 or greater, always round up. So 1350 rounds to 1400, and 1367 also rounds to 1400.

Q: How do I remember which digit to check?

Look one place to the right of where you're rounding! Rounding to hundreds? Check the tens place. Rounding to tens? Check the units place.

Q: Why does 1367 become 1400 and not 1370?

Because we're rounding to the nearest hundred, not the nearest ten. We replace both the tens and units digits with zeros: 1367 → 1400.

Q: How can I double-check my rounding?

1367 is closer to 1400 than to 1300Distance to 1300: $ 1367 - 1300 = 67 $Distance to 1400: $ 1400 - 1367 = 33 $Since 33 1400 is correct!

Rounding Numbers with Hundreds Place

$1367\approx\text{ ?}$

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Step-by-step written solution

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Understand the problem

$1367\approx\text{ ?}$

Step-by-step solution

To round the number 1367 to the nearest hundred, we carry out the following steps:

Step 1: Identify the digit in the tens place, which is '6' for 1367.
Step 2: Apply the rounding rule where if the tens digit is 5 or greater, round up.
Step 3: Since the tens digit is 6, we round up.
Step 4: Replace the tens and units digits with zero.
This results in rounding 1367 to 1400.

Thus, when rounding 1367 to the nearest hundred, we get $1400$ .

Final Answer

$1400$

Key Points to Remember

Essential concepts to master this topic

Rule: Look at tens digit to round to nearest hundred
Technique: Since tens digit 6 ≥ 5, round 1367 up to 1400
Check: Verify 1400 is closer to 1367 than 1300 ✓

Common Mistakes

Avoid these frequent errors

Looking at the units digit instead of tens digit
Don't look at the 7 in the units place = wrong rounding direction! The units digit doesn't determine hundreds place rounding. Always examine the tens digit (6 in 1367) to decide whether to round up or down.

Practice Quiz

Test your knowledge with interactive questions

$134\approx\text{ ?}$

FAQ

Everything you need to know about this question

Why do I look at the tens digit and not the units digit?

When rounding to the nearest hundred, the tens digit tells you which hundred is closer. The units digit only matters when rounding to the nearest ten!

What happens if the tens digit is exactly 5?

When the tens digit is 5 or greater, always round up. So 1350 rounds to 1400, and 1367 also rounds to 1400.

How do I remember which digit to check?

Look one place to the right of where you're rounding! Rounding to hundreds? Check the tens place. Rounding to tens? Check the units place.

Why does 1367 become 1400 and not 1370?

Because we're rounding to the nearest hundred, not the nearest ten. We replace both the tens and units digits with zeros: 1367 → 1400.

How can I double-check my rounding?

1367 is closer to 1400 than to 1300
Distance to 1300: $1367 - 1300 = 67$
Distance to 1400: $1400 - 1367 = 33$

Since 33 < 67, 1400 is correct!

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