Solve Division Problem: 65.2 ÷ 10 Using Decimal Place Values

Q: Why does dividing by 10 move the decimal point left?

Think of it this way: dividing makes numbers smaller. Moving the decimal point left makes each digit worth 10 times less, which is exactly what happens when you divide by 10!

Q: What if there aren't enough digits to move the decimal?

Add zeros to the left! For example, $ 3.4 ÷ 10 $ becomes $ 0.34 $. The zero acts as a placeholder to show the decimal moved left.

Q: How do I remember which direction to move the decimal?

Dividing by 10, 100, 1000: Move decimal LEFT (numbers get smaller)Multiplying by 10, 100, 1000: Move decimal RIGHT (numbers get bigger)

Q: Can I check my answer without multiplying back?

Yes! Think logically: $ 65.2 ÷ 10 $ should give you something close to 6 or 7 since 60 ÷ 10 = 6. If you got 65.2 or 652, you know something went wrong!

Q: What's the pattern for dividing by 100 or 1000?

Dividing by 100: Move decimal 2 places leftDividing by 1000: Move decimal 3 places leftThe number of zeros tells you how many places to move!

Decimal Division with Place Value Shifts

$65.2:10=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:08 Count the number of zeros.

00:13 Now, move the decimal point that many spaces.

00:21 And that's the solution! Great job.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$65.2:10=$

Step-by-step solution

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

Step 1: Identify the given number, which is $65.2$ .
Step 2: Apply the rule for dividing a decimal by 10: Shift the decimal point one place to the left.
Step 3: Verify the result by ensuring the computation is accurate.

Now, let's work through each step:
Step 1: The problem gives us the number $65.2$ .
Step 2: We'll divide by 10 by shifting the decimal point one place left. This changes $65.2$ to $6.52$ .
Step 3: Checking our work, $6.52$ is indeed the correct result of shifting the decimal point left.

Therefore, the solution to the problem is $6.52$ .

Final Answer

$6.52$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by 10 shifts the decimal point one place left
Technique: Move 65.2's decimal from after 2 to between 5 and 2
Check: Multiply result back: $6.52 \times 10 = 65.2$ ✓

Common Mistakes

Avoid these frequent errors

Moving the decimal point in the wrong direction
Don't move the decimal point right when dividing by 10 = 652.0 instead of 6.52! This makes the number larger instead of smaller. Always remember: dividing makes numbers smaller, so move the decimal point LEFT.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why does dividing by 10 move the decimal point left?

Think of it this way: dividing makes numbers smaller. Moving the decimal point left makes each digit worth 10 times less, which is exactly what happens when you divide by 10!

What if there aren't enough digits to move the decimal?

Add zeros to the left! For example, $3.4 ÷ 10$ becomes $0.34$ . The zero acts as a placeholder to show the decimal moved left.

How do I remember which direction to move the decimal?

Dividing by 10, 100, 1000: Move decimal LEFT (numbers get smaller)
Multiplying by 10, 100, 1000: Move decimal RIGHT (numbers get bigger)

Can I check my answer without multiplying back?

Yes! Think logically: $65.2 ÷ 10$ should give you something close to 6 or 7 since 60 ÷ 10 = 6. If you got 65.2 or 652, you know something went wrong!

What's the pattern for dividing by 100 or 1000?

Dividing by 100: Move decimal 2 places left
Dividing by 1000: Move decimal 3 places left
The number of zeros tells you how many places to move!

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