Solve Decimal Multiplication: 0.1 × 0.999 Step by Step

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

This is the fundamental rule for decimal multiplication! When you multiply decimals, the total number of decimal places in your answer equals the sum of decimal places in both factors.

Q: What if I don't have enough digits for all the decimal places?

Add leading zeros! In this problem, 999 needs 4 decimal places, so it becomes $ 0.0999 $ with a zero added at the front.

Q: Can I use a calculator to check my work?

Absolutely! Calculate $ 0.1 \times 0.999 $ on your calculator. You should get $ 0.0999 $ to confirm your manual calculation.

Q: Is there a pattern when multiplying by 0.1?

Yes! Multiplying by $ 0.1 $ is the same as dividing by 10, which moves the decimal point one place to the left: $ 0.999 \div 10 = 0.0999 $

Q: What if one number has no decimal places?

Whole numbers have zero decimal places! For example, $ 5 \times 0.23 $ would have $ 0 + 2 = 2 $ decimal places in the answer.

Decimal Multiplication with Place Value Positioning

$0.1\times0.999=$

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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

00:08 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

$0.1\times0.999=$

Step-by-step solution

To solve $0.1 \times 0.999$ , we need to follow these steps carefully:

Step 1: Treat the numbers as integers and multiply them. Ignoring the decimal points temporarily, multiply $1$ by $999$ :
$\quad 1 \times 999 = 999$ .
Step 2: Determine the total number of decimal places in the factors.
$\quad 0.1$ has 1 decimal place.
$\quad 0.999$ has 3 decimal places.
Therefore, the product should have $1 + 3 = 4$ decimal places.
Step 3: Position the decimal in the product calculated in step 1.
$\quad 999$ with 4 decimal places becomes $0.0999$ .

Therefore, the product of $0.1 \times 0.999$ is $0.0999$ .

Final Answer

$0.0999$

Key Points to Remember

Essential concepts to master this topic

Rule: Add decimal places from both factors for final result
Technique: $1 \times 999 = 999$ , then place decimal 4 positions left
Check: Count decimal places: 0.1 (1) + 0.999 (3) = 4 total ✓

Common Mistakes

Avoid these frequent errors

Incorrectly counting or placing decimal positions
Don't just guess where the decimal goes = $9.99$ or $0.999$ ! This ignores the multiplication rule for decimals. Always count total decimal places in both factors (1 + 3 = 4) and place the decimal that many positions from the right.

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?

This is the fundamental rule for decimal multiplication! When you multiply decimals, the total number of decimal places in your answer equals the sum of decimal places in both factors.

What if I don't have enough digits for all the decimal places?

Add leading zeros! In this problem, 999 needs 4 decimal places, so it becomes $0.0999$ with a zero added at the front.

Can I use a calculator to check my work?

Absolutely! Calculate $0.1 \times 0.999$ on your calculator. You should get $0.0999$ to confirm your manual calculation.

Is there a pattern when multiplying by 0.1?

Yes! Multiplying by $0.1$ is the same as dividing by 10, which moves the decimal point one place to the left: $0.999 \div 10 = 0.0999$

What if one number has no decimal places?

Whole numbers have zero decimal places! For example, $5 \times 0.23$ would have $0 + 2 = 2$ decimal places in the answer.

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