Solve: Multiplying 3.2 × 10 Using Decimal Operations

Q: Why does multiplying by 10 move the decimal point?

Multiplying by 10 means making the number ten times larger. Moving the decimal point one place right is the fastest way to make any decimal ten times bigger!

Q: What happens to the zero after the decimal point?

When $ 3.2 $ becomes $ 32.0 $, the trailing zero isn't needed. We write it as 32 because trailing zeros after decimals don't change the value.

Q: Does this work for multiplying by 100 or 1000?

Absolutely! For 100, move the decimal two places right. For 1000, move it three places right. The pattern is: one zero = one decimal place!

Q: What if I don't see a decimal point in my answer?

That's normal! When $ 3.2 \times 10 = 32 $, we get a whole number. The decimal point is there invisibly: 32.0, but we don't write it.

Q: How do I check if 32 is really correct?

Use division! Since $ 32 \div 10 = 3.2 $, our answer checks out perfectly. Division is the opposite of multiplication.

Decimal Multiplication with Powers of Ten

$3.2\times10=$

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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.

00:07 Count the number of zeros, then move the decimal point, step by step.

00:12 Carefully move the decimal point, based on the zeros you counted.

00:20 And that's how we find our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3.2\times10=$

Step-by-step solution

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

Step 1: Identify the number to be multiplied, which is $3.2$ .
Step 2: Apply the rule for multiplying decimals by powers of 10, which shifts the decimal point to the right.
Step 3: Perform the multiplication and verify against the answer choices provided.

Now, let's work through each step:

Step 1: We have the number $3.2$ .
Step 2: By multiplying by 10, we move the decimal point one position to the right, changing $3.2$ to $32.0$ . Given that trailing zeros in decimals are not necessary, $32.0$ is equal to $32$ .

Step 3: Comparing against the answer choices $32$ , $34$ , $36$ , and $38$ , the correct answer is clearly $32$ .

Therefore, the solution to the problem is $32$ .

Final Answer

$32$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplying by 10 moves decimal point one place right
Technique: Change 3.2 to 32 by shifting decimal: 3.2 → 32.0
Check: Verify 32 ÷ 10 = 3.2, confirming our multiplication ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying by powers of 10
Don't add 10 to 3.2 to get 13.2! This completely ignores the multiplication operation. Always remember that multiplication by 10 shifts the decimal point, not adds to the number.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does multiplying by 10 move the decimal point?

Multiplying by 10 means making the number ten times larger. Moving the decimal point one place right is the fastest way to make any decimal ten times bigger!

What happens to the zero after the decimal point?

When $3.2$ becomes $32.0$ , the trailing zero isn't needed. We write it as 32 because trailing zeros after decimals don't change the value.

Does this work for multiplying by 100 or 1000?

Absolutely! For 100, move the decimal two places right. For 1000, move it three places right. The pattern is: one zero = one decimal place!

What if I don't see a decimal point in my answer?

That's normal! When $3.2 \times 10 = 32$ , we get a whole number. The decimal point is there invisibly: 32.0, but we don't write it.

How do I check if 32 is really correct?

Use division! Since $32 \div 10 = 3.2$ , our answer checks out perfectly. Division is the opposite of multiplication.

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