Solve Decimal Multiplication: 0.1 × 0.35 Step-by-Step

Q: Why do I add the decimal places together?

When multiplying decimals, you're multiplying very small parts. $ 0.1 $ means 1 tenth, and $ 0.35 $ means 35 hundredths. Multiplying these gives you thousandths, so you need 3 decimal places total!

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

Try this trick: ignore the decimals completely and multiply 1 × 35 = 35. Then count decimal places in the original numbers (1 + 2 = 3) and put the decimal point 3 places from the right: 0.035.

Q: Can I convert to fractions instead?

Absolutely! $ 0.1 = \frac{1}{10} $ and $ 0.35 = \frac{35}{100} $. Then $ \frac{1}{10} \times \frac{35}{100} = \frac{35}{1000} = 0.035 $. This confirms our answer!

Q: Why isn't 0.35 the right answer?

Think about it logically: you're multiplying 0.35 by something less than 1 (which is 0.1). The result must be smaller than 0.35, not equal to it. That's why 0.035 makes sense!

Q: What if one number has no visible decimal places?

Numbers like 5 actually have zero decimal places (same as 5.0). So if you multiply 5 × 0.23, you count 0 + 2 = 2 decimal places in your answer.

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 add one zero

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$0.1\times0.35=$

2

Step-by-step solution

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

Step 1: Convert the decimal numbers into a form that is easier to multiply.
Step 2: Multiply the numbers as if they were whole numbers.
Step 3: Adjust the product by placing the decimal point correctly.

Now, let's work through each step:

Step 1: Convert the decimals $0.1$ and $0.35$ into whole number expressions:

$0.1$ can be thought of as $\frac{1}{10}$ .
$0.35$ can be thought of as $\frac{35}{100}$ .

Step 2: Multiply as whole numbers: Multiply $1$ and $35$ to obtain $35$ .

Step 3: Adjust the decimal point:

$0.1$ has 1 decimal place.
$0.35$ has 2 decimal places.

Thus, their product should have

1 + 2 = 3

decimal places.

Therefore, the product of $0.1$ and $0.35$ is $0.035$ .

Looking at the choices provided:

Choice 1: $0.35$ is incorrect as it does not consider the decimal adjustment.
Choice 2: $0.035$ is correct.
Choice 3: $0.350$ is incorrect as it has an extra zero and maintains the incorrect placement of the decimal point.
Choice 4: $0.310$ is incorrect as it does not correspond with the straightforward multiplication of the operands.

Thus, the correct choice is $0.035$ .

3

Final Answer

$0.035$

Key Points to Remember

Essential concepts to master this topic

Rule: Add decimal places from both numbers for final answer
Technique: Multiply 1 × 35 = 35, then place 3 decimal places
Check: Count decimal places: 0.1 (1 place) + 0.35 (2 places) = 3 total ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count decimal places correctly
Don't just multiply 0.1 × 0.35 = 0.35 by ignoring decimal placement! This gives the wrong answer because you're not accounting for how small the numbers really are. Always count decimal places in both numbers (1 + 2 = 3) and place that many in your final answer.

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 add the decimal places together?

+

When multiplying decimals, you're multiplying very small parts. $0.1$ means 1 tenth, and $0.35$ means 35 hundredths. Multiplying these gives you thousandths, so you need 3 decimal places total!

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

+

Try this trick: ignore the decimals completely and multiply 1 × 35 = 35. Then count decimal places in the original numbers (1 + 2 = 3) and put the decimal point 3 places from the right: 0.035.

Can I convert to fractions instead?

+

Absolutely! $0.1 = \frac{1}{10}$ and $0.35 = \frac{35}{100}$ . Then $\frac{1}{10} \times \frac{35}{100} = \frac{35}{1000} = 0.035$ . This confirms our answer!

Why isn't 0.35 the right answer?

+

Think about it logically: you're multiplying 0.35 by something less than 1 (which is 0.1). The result must be smaller than 0.35, not equal to it. That's why 0.035 makes sense!

What if one number has no visible decimal places?

+

Numbers like 5 actually have zero decimal places (same as 5.0). So if you multiply 5 × 0.23, you count 0 + 2 = 2 decimal places in your answer.

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