Solve the Decimal Multiplication: 2.78 × 10 Step by Step

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

Multiplying by 10 means making something 10 times bigger. Moving the decimal point right increases each digit's place value by 10, which is exactly what multiplication by 10 does!

Q: What if I multiply by 100 or 1000?

The pattern continues! For 100, move the decimal point 2 places right. For 1000, move it 3 places right. Count the zeros to know how many places to move.

Q: What happens if there aren't enough decimal places?

Add zeros as placeholders! For example, $ 2.7 \times 100 $ becomes $ 2.70 \times 100 = 270 $.

Q: How can I check my answer without a calculator?

Think about it logically: $ 2.78 $ is almost 3, and $ 3 \times 10 = 30 $. So $ 27.8 $ makes sense because it's close to 30!

Q: Does this work for multiplying by 0.1 or 0.01?

Yes, but in reverse! Multiplying by 0.1 moves the decimal point one place left. It's like dividing by 10. So $ 2.78 \times 0.1 = 0.278 $.

Decimal Multiplication with Powers of Ten

$2.78\times10=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 According to the number of zeros, move the decimal point

00:08 Move the decimal point as many places as zeros

00:19 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

$2.78\times10=$

Step-by-step solution

To solve multiplying the decimal number $2.78$ by $10$ , we'll apply the rule of moving the decimal point:

Step 1: Identify the decimal number, which is $2.78$ .
Step 2: Recognize that when multiplying by $10$ , the decimal point shifts one place to the right.

By shifting the decimal point one position right, $2.78$ becomes $27.8$ .

This operation shows that multiplying by $10$ effectively scales the value up by one power of ten.

Therefore, the solution to the problem is $27.8$ .

Final Answer

$\text{27}.8$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplying by 10 shifts decimal point one place right
Technique: Move decimal point in $2.78$ from 2.78 to 27.8
Check: Count decimal places: original 2 places, result 1 place ✓

Common Mistakes

Avoid these frequent errors

Moving the decimal point the wrong direction
Don't move the decimal point left when multiplying by 10 = getting 0.278 instead of 27.8! Moving left makes numbers smaller, but multiplication should make them bigger. Always move the decimal point RIGHT when multiplying by powers of 10.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does the decimal point move when multiplying by 10?

Multiplying by 10 means making something 10 times bigger. Moving the decimal point right increases each digit's place value by 10, which is exactly what multiplication by 10 does!

What if I multiply by 100 or 1000?

The pattern continues! For 100, move the decimal point 2 places right. For 1000, move it 3 places right. Count the zeros to know how many places to move.

What happens if there aren't enough decimal places?

Add zeros as placeholders! For example, $2.7 \times 100$ becomes $2.70 \times 100 = 270$ .

How can I check my answer without a calculator?

Think about it logically: $2.78$ is almost 3, and $3 \times 10 = 30$ . So $27.8$ makes sense because it's close to 30!

Does this work for multiplying by 0.1 or 0.01?

Yes, but in reverse! Multiplying by 0.1 moves the decimal point one place left. It's like dividing by 10. So $2.78 \times 0.1 = 0.278$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime