Calculate the Product: 0.1 × 7.33 Decimal Multiplication

Q: Why do I multiply 10 × 733 instead of 0.1 × 7.33 directly?

Multiplying whole numbers first makes the calculation much easier! You avoid decimal confusion during multiplication, then just place the decimal point correctly at the end using the place value rule.

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

Always move the decimal point left (toward smaller numbers) when you're putting it back. Count the total decimal places in your factors, then move that many spots left from the right end.

Q: What if I get confused counting decimal places?

Write it out step by step: 0.1 has 1 decimal place, 7.33 has 2 decimal places. Add them: 1 + 2 = 3 total. Your answer must have exactly 3 decimal places.

Q: Can I check my answer a different way?

Yes! Think about it logically: $ 0.1 $ means "one-tenth," so $ 0.1 \times 7.33 $ should be one-tenth of 7.33, which is 0.733.

Q: Why is 7.33 wrong if it's close to the original number?

7.33 is too big! When you multiply by 0.1, you're making the number smaller, not keeping it the same size. 0.1 × 7.33 must be less than 7.33.

Decimal Multiplication with Place Value Alignment

$0.1\times7.33=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Convert decimal number to fraction

00:10 There is only one zero in the denominator, so we'll move the decimal point once

00:18 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

$0.1\times7.33=$

Step-by-step solution

Let's solve the problem of multiplying $0.1$ and $7.33$ step by step.

Step 1: Rewrite the two numbers without considering the decimal points. Calculate the product of 10 and 733.

Step 2: The result of $10 \times 733$ is $7330$ .

Step 3: Count the total number of decimal places in the original factors $0.1$ and $7.33$ .
- $0.1$ has 1 decimal place.
- $7.33$ has 2 decimal places.
Together, they amount to 3 decimal places.

Step 4: In the product $7330$ , move the decimal point backwards to account for the 3 decimal places. So, the decimal point goes three places from the end of the number.

The result is $0.733$ .

Therefore, $0.1 \times 7.33 = 0.733$ .

The correct answer choice is $0.733$ .

Final Answer

$0.733$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total decimal places in both factors combined
Technique: Multiply 10 × 733 = 7330, then place decimal
Check: Verify 0.1 × 7.33 = 0.733 has 3 decimal places ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count decimal places correctly
Don't just multiply 1 × 733 = 733 and guess where the decimal goes! This ignores place value rules and gives wrong answers like 7.33 or 73.3. Always count total decimal places (0.1 has 1, 7.33 has 2, so 3 total) and move decimal point that many places left.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 0.008 =$

FAQ

Everything you need to know about this question

Why do I multiply 10 × 733 instead of 0.1 × 7.33 directly?

Multiplying whole numbers first makes the calculation much easier! You avoid decimal confusion during multiplication, then just place the decimal point correctly at the end using the place value rule.

How do I remember which direction to move the decimal point?

Always move the decimal point left (toward smaller numbers) when you're putting it back. Count the total decimal places in your factors, then move that many spots left from the right end.

What if I get confused counting decimal places?

Write it out step by step: 0.1 has 1 decimal place, 7.33 has 2 decimal places. Add them: 1 + 2 = 3 total. Your answer must have exactly 3 decimal places.

Can I check my answer a different way?

Yes! Think about it logically: $0.1$ means "one-tenth," so $0.1 \times 7.33$ should be one-tenth of 7.33, which is 0.733.

Why is 7.33 wrong if it's close to the original number?

7.33 is too big! When you multiply by 0.1, you're making the number smaller, not keeping it the same size. 0.1 × 7.33 must be less than 7.33.

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