Solve Decimal Multiplication: 0.1 × 74.8 Step by Step

Q: What if I get confused about where to put the decimal point?

Use this trick: multiply the numbers without decimal points first, then count the total decimal places from both original numbers and place the decimal point that many places from the right.

Q: Can I think of 0.1 as 1/10 to make it easier?

Absolutely! $ 0.1 = \frac{1}{10} $, so $ 0.1 \times 74.8 = \frac{74.8}{10} = 7.48 $. This is a great way to check your work!

Q: What if my answer has trailing zeros?

You can usually remove trailing zeros after the decimal point. For example, 7.480 becomes 7.48. However, in some contexts (like money), you might keep them.

Q: How can I estimate to check if my answer makes sense?

Round first: $ 0.1 \times 75 \approx 7.5 $. Since 7.48 is close to 7.5, your answer is reasonable!

Decimal Multiplication with Place Value Management

$0.1\times74.8=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert from decimal to fraction

00:15 There is only one zero in the denominator, so we'll move the decimal point once

00:21 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

$0.1\times74.8=$

Step-by-step solution

To solve this problem, let's follow these steps:

Identify and Analyze Decimal Places: Both numbers $0.1$ and $74.8$ have decimal points. Specifically, $0.1$ has one decimal place, and $74.8$ has one decimal place, making a total of two decimal places.
Perform Multiplication: Multiply the numbers as if they were whole numbers. Ignoring decimal points, multiply $1 \times 748$ , which equals $748$ .
Place the Decimal Point: Since the multiplication involves two decimal places in total (one from each factor), the product $748$ should be adjusted to have two decimal places. Thus, it becomes $7.48$ .

Thus, the result of multiplying $0.1 \times 74.8$ is $\mathbf{7.48}$ .

The correct answer is choice 2: $\mathbf{7.48}$ .

Final Answer

$7.48$

Key Points to Remember

Essential concepts to master this topic

Decimal Rule: Total decimal places in factors equals decimal places in product
Technique: Multiply 1 × 748 = 748, then place decimal for 7.48
Check: Count decimal places: 0.1 (1) + 74.8 (1) = 7.48 (2) ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count decimal places correctly
Don't just multiply 0.1 × 74.8 = 74.8 by ignoring place values! This gives 74.8 instead of 7.48 because you're not accounting for the decimal positions properly. Always count total decimal places from both numbers and place the decimal point correctly in your answer.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 4.35 =$

FAQ

Everything you need to know about this question

Why do I need to count decimal places in both numbers?

Each decimal place represents a power of 10. When multiplying decimals, you're essentially multiplying by tenths, hundredths, etc. The total decimal places tell you the final position of your decimal point.

What if I get confused about where to put the decimal point?

Use this trick: multiply the numbers without decimal points first, then count the total decimal places from both original numbers and place the decimal point that many places from the right.

Can I think of 0.1 as 1/10 to make it easier?

Absolutely! $0.1 = \frac{1}{10}$ , so $0.1 \times 74.8 = \frac{74.8}{10} = 7.48$ . This is a great way to check your work!

What if my answer has trailing zeros?

You can usually remove trailing zeros after the decimal point. For example, 7.480 becomes 7.48. However, in some contexts (like money), you might keep them.

How can I estimate to check if my answer makes sense?

Round first: $0.1 \times 75 \approx 7.5$ . Since 7.48 is close to 7.5, your answer is reasonable!

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