Multiply Decimals: Calculate 0.1 × 0.004 Step-by-Step

Q: Why do I add the decimal places instead of multiplying them?

When multiplying decimals, you add the number of decimal places because each decimal place represents a factor of 10. Think of it as: $ 0.1 = \frac{1}{10} $ and $ 0.004 = \frac{4}{1000} $, so the product has 1 + 3 = 4 decimal places.

Q: What if I get confused counting decimal places?

Try this trick: underline each digit after the decimal point in both numbers. In 0.1, underline the 1 (that's 1 place). In 0.004, underline 0, 0, 4 (that's 3 places). Total: 1 + 3 = 4 places!

Q: Can I just ignore the decimals and add them back later?

Yes! This is actually a great strategy. Multiply 1 × 4 = 4, then place the decimal to get 4 total decimal places: $ 0.0004 $. Just don't forget the final decimal placement step!

Q: How do I know if 0.0004 is reasonable?

Use estimation! $ 0.1 $ is about $ \frac{1}{10} $ and $ 0.004 $ is very small. So $ \frac{1}{10} $ of something very small should be extremely small - and 0.0004 is indeed very small!

Q: What if my answer has trailing zeros?

Keep them if they're significant! In $ 0.0004 $, all zeros show the decimal place position. However, if you got 0.4000, you could write it as 0.4 since trailing zeros after the decimal don't change the value.

Decimal Multiplication with Multiple Decimal Places

$0.1\times0.004=$

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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 number to fraction

00:09 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

Understand the problem

$0.1\times0.004=$

Step-by-step solution

To solve this problem, we'll multiply the decimals as follows:

Step 1: Multiply the whole numbers 1 and 4. This gives us 4.
Step 2: Count the total number of decimal places in the factors. $0.1$ has 1 decimal place, and $0.004$ has 3 decimal places.
Step 3: In the final answer, place the decimal point to ensure our product has $1 + 3 = 4$ decimal places.

Now, let's apply these steps:

First, multiply 1 by 4 to get 4. Then place the decimal in the product so it has 4 decimal places: $0.0004$ .

Therefore, the solution to the problem is $0.0004$ .

Final Answer

$0.0004$

Key Points to Remember

Essential concepts to master this topic

Rule: Add decimal places from both factors for final answer
Technique: Multiply 1 × 4 = 4, then count 1 + 3 = 4 decimal places
Check: Count digits after decimal: 0.0004 has exactly 4 decimal places ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all decimal places
Don't just multiply 1 × 4 = 4 and guess where the decimal goes = wrong answer like 0.4 or 0.04! This ignores the precision of the original numbers. Always count decimal places in both factors and add them together for the final placement.

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 instead of multiplying them?

When multiplying decimals, you add the number of decimal places because each decimal place represents a factor of 10. Think of it as: $0.1 = \frac{1}{10}$ and $0.004 = \frac{4}{1000}$ , so the product has 1 + 3 = 4 decimal places.

What if I get confused counting decimal places?

Try this trick: underline each digit after the decimal point in both numbers. In 0.1, underline the 1 (that's 1 place). In 0.004, underline 0, 0, 4 (that's 3 places). Total: 1 + 3 = 4 places!

Can I just ignore the decimals and add them back later?

Yes! This is actually a great strategy. Multiply 1 × 4 = 4, then place the decimal to get 4 total decimal places: $0.0004$ . Just don't forget the final decimal placement step!

How do I know if 0.0004 is reasonable?

Use estimation! $0.1$ is about $\frac{1}{10}$ and $0.004$ is very small. So $\frac{1}{10}$ of something very small should be extremely small - and 0.0004 is indeed very small!

What if my answer has trailing zeros?

Keep them if they're significant! In $0.0004$ , all zeros show the decimal place position. However, if you got 0.4000, you could write it as 0.4 since trailing zeros after the decimal don't change the value.

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