Solve Decimal Division: 30.3 ÷ 300 Step by Step

Q: Why can't I just move the decimal point in 30.3?

Moving decimal points only works for powers of 10 (like 10, 100, 1000). Since 300 = 3 × 100, you need to divide by 3 first, then handle the factor of 100.

Q: What if I get 0.1 instead of 0.101?

Check your work! $ 0.1 \times 300 = 30 $, not 30.3. You likely forgot about the 0.3 part of the dividend. Remember: $ 30.3 \div 3 = 10.1 $, not 10.

Q: Why does moving the decimal two places work for dividing by 100?

Dividing by 100 is the opposite of multiplying by 100. Just like multiplying by 100 moves the decimal right two places, dividing moves it left two places.

Q: Can I use long division instead?

Yes, but factoring is faster! Long division with $ 30.3 \div 300 $ requires more steps. The factoring method breaks down the problem into easier pieces.

Q: How do I verify my answer is exactly right?

Multiply your answer by the original divisor: $ 0.101 \times 300 $. If you get back to 30.3 exactly, your answer is correct!

Decimal Division with Multi-Step Factorization

$30.3:300=$

❤️ 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 Multiply each factor by 100 to eliminate the decimal point

00:39 Convert division to fraction

00:46 Break down each factor into factors with multiplication of 3

00:54 Reduce what's possible

01:03 According to the number of zeros in the denominator, we'll move the decimal point

01:18 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

$30.3:300=$

Step-by-step solution

To solve this problem, we will follow these steps:

Understand the context and arithmetic implication of dividing by $300$ .
Apply the division rule for decimal fractions to manage decimal point movements effectively.
Verify calculated results with given choices.

Step 1: We know that we need to divide $30.3$ by $300$ . To do this, observe that:

Step 2: The number $300$ can be written as $3 \times 100$ . When we divide by $300$ , it's equivalent to:

First dividing $30.3$ by $3$ .
Then dividing the result by $100$ (which is moving the decimal point two places to the left).

Step 3: Perform the calculation:
- $30.3 \div 3 = 10.1$ .
- Now divide $10.1$ by $100$ , which effectively moves the decimal two places left, giving $0.101$ .

Therefore, the solution to the problem is $0.101$ .

Final Answer

$0.101$

Key Points to Remember

Essential concepts to master this topic

Rule: Factor the divisor to simplify decimal division steps
Technique: Write 300 as 3 × 100, then divide 30.3 ÷ 3 = 10.1
Check: Multiply back: 0.101 × 300 = 30.3 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point without proper division steps
Don't just move the decimal point randomly or use shortcuts without understanding = wrong answer like 0.1! This ignores the actual division process and mathematical relationships. Always break down the divisor systematically and perform each division step clearly.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just move the decimal point in 30.3?

Moving decimal points only works for powers of 10 (like 10, 100, 1000). Since 300 = 3 × 100, you need to divide by 3 first, then handle the factor of 100.

How do I know when to factor the divisor?

Factor when the divisor isn't a simple power of 10! For 300, factoring into 3 × 100 makes the division much clearer than trying to divide by 300 directly.

What if I get 0.1 instead of 0.101?

Check your work! $0.1 \times 300 = 30$ , not 30.3. You likely forgot about the 0.3 part of the dividend. Remember: $30.3 \div 3 = 10.1$ , not 10.

Why does moving the decimal two places work for dividing by 100?

Dividing by 100 is the opposite of multiplying by 100. Just like multiplying by 100 moves the decimal right two places, dividing moves it left two places.

Can I use long division instead?

Yes, but factoring is faster! Long division with $30.3 \div 300$ requires more steps. The factoring method breaks down the problem into easier pieces.

How do I verify my answer is exactly right?

Multiply your answer by the original divisor: $0.101 \times 300$ . If you get back to 30.3 exactly, your answer is correct!

🌟 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