Calculate the Product: 0.1 × 3.5 Decimal Multiplication

Q: Why do I ignore the decimal points when multiplying first?

Ignoring decimals initially makes the multiplication easier! You multiply $ 1 \times 35 = 35 $ as whole numbers, then use the decimal place rule to position the decimal correctly.

Q: What if one number has no decimal places?

A whole number like 5 actually has zero decimal places. So $ 0.2 \times 5 $ would have 1 + 0 = 1 decimal place in the answer.

Q: How do I remember the decimal place rule?

Think: "Add the decimal places, place the dot!" Count decimal places in both numbers, add them together, then count that many places from the right in your product.

Q: Can I check my answer a different way?

Yes! You can think of it as fractions: $ 0.1 = \frac{1}{10} $ and $ 3.5 = \frac{35}{10} $, so $ \frac{1}{10} \times \frac{35}{10} = \frac{35}{100} = 0.35 $

Decimal Multiplication with Place Value Counting

$0.1\times3.5=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert decimal number to fraction

00:14 There is only one zero in the denominator, so we'll move the decimal point once

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

$0.1\times3.5=$

Step-by-step solution

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

Step 1: Multiply the numbers without considering the decimal point.
Step 2: Count the total number of decimal places in the numbers being multiplied.
Step 3: Position the decimal point in the product accordingly.

Now, let's work through each step:

Step 1: Multiply $0.1$ by $3.5$ as whole numbers $1 \times 35 = 35$ .

Step 2: Count the decimal places: $0.1$ has 1 decimal place, and $3.5$ has 1 decimal place, totaling 2 decimal places.

Step 3: In the product $35$ , place the decimal point such that there are 2 decimal places: This gives us $0.35$ .

Therefore, the solution to the problem is $0.35$ .

Final Answer

$0.35$

Key Points to Remember

Essential concepts to master this topic

Rule: Total decimal places in factors equals decimal places in product
Technique: Multiply 1 × 35 = 35, then place decimal after 2 places
Check: Count decimal places: 0.1 (1) + 3.5 (1) = 0.35 (2 places) ✓

Common Mistakes

Avoid these frequent errors

Placing decimal point incorrectly in the product
Don't just guess where the decimal goes or put it in the wrong position = answers like 3.5 or 0.035! This happens when you don't count total decimal places from both numbers. Always count decimal places in both factors (0.1 has 1, 3.5 has 1) and place the decimal so your answer has exactly 2 places.

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 ignore the decimal points when multiplying first?

Ignoring decimals initially makes the multiplication easier! You multiply $1 \times 35 = 35$ as whole numbers, then use the decimal place rule to position the decimal correctly.

What if one number has no decimal places?

A whole number like 5 actually has zero decimal places. So $0.2 \times 5$ would have 1 + 0 = 1 decimal place in the answer.

How do I remember the decimal place rule?

Think: "Add the decimal places, place the dot!" Count decimal places in both numbers, add them together, then count that many places from the right in your product.

What if my answer starts with zeros like 0.35?

That's correct! When your product needs more decimal places than digits, you add zeros to the left. For example, 35 with 2 decimal places becomes 0.35.

Can I check my answer a different way?

Yes! You can think of it as fractions: $0.1 = \frac{1}{10}$ and $3.5 = \frac{35}{10}$ , so $\frac{1}{10} \times \frac{35}{10} = \frac{35}{100} = 0.35$

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