Solve: 0.3 × 10 - Decimal Multiplication with Powers of Ten

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

Think of it this way: 10 has one zero, so the decimal moves one place right. This makes the number 10 times bigger! $ 0.3 \times 10 = 3 $

Q: What if there's no decimal point shown in my answer?

That's normal! When $ 0.3 \times 10 = 3 $, we write just 3 instead of 3.0 because whole numbers don't need decimal points.

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

Yes! Count the zeros in the multiplier. 100 has 2 zeros = move decimal 2 places right. 1000 has 3 zeros = move decimal 3 places right.

Q: What happens if I don't have enough digits to move the decimal?

Add zeros! For example, $ 0.3 \times 100 $ becomes 030, which equals 30. The zeros help you move the decimal correctly.

Q: How can I double-check my work?

Use division to check! If $ 0.3 \times 10 = 3 $, then $ 3 ÷ 10 $ should equal 0.3. Try it!

Decimal Multiplication with Simple Shifts

$0.3\times10=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the number of zeros, move the decimal point

00:09 Move the decimal point according to the number of zeros

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$0.3\times10=$

Step-by-step solution

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

Step 1: Understand the operation needed: multiply the decimal 0.3 by 10.
Step 2: Apply the rule for multiplying by powers of 10.
Step 3: Execute the operation and write down the result.

Now, let's work through each step:
Step 1: We need to multiply 0.3 by 10. Multiplying by 10 involves shifting the decimal point.
Step 2: Using the rule for multiplying decimals by 10, we shift the decimal point in 0.3 one place to the right.
Step 3: Originally, the decimal point in 0.3 is after the '3'. After shifting it right by one place, we get '3.0'. This is equivalent to $3$ .

Therefore, the solution to the problem is $3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplying by 10 shifts decimal point one place right
Technique: Move decimal in 0.3 right once to get 3.0
Check: Verify 3 ÷ 10 equals original 0.3 ✓

Common Mistakes

Avoid these frequent errors

Adding zero instead of shifting decimal point
Don't think 0.3 × 10 means adding a zero to get 0.30 = wrong answer stays 0.3! This ignores the multiplication entirely. Always shift the decimal point one place to the right when multiplying by 10.

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?

Think of it this way: 10 has one zero, so the decimal moves one place right. This makes the number 10 times bigger! $0.3 \times 10 = 3$

What if there's no decimal point shown in my answer?

That's normal! When $0.3 \times 10 = 3$ , we write just 3 instead of 3.0 because whole numbers don't need decimal points.

Does this work for multiplying by 100 or 1000?

Yes! Count the zeros in the multiplier. 100 has 2 zeros = move decimal 2 places right. 1000 has 3 zeros = move decimal 3 places right.

What happens if I don't have enough digits to move the decimal?

Add zeros! For example, $0.3 \times 100$ becomes 030, which equals 30. The zeros help you move the decimal correctly.

How can I double-check my work?

Use division to check! If $0.3 \times 10 = 3$ , then $3 ÷ 10$ should equal 0.3. Try it!

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