Solve Decimal Multiplication: 0.01 × 285.11 Step-by-Step

Q: Why do I add the decimal places together?

When multiplying decimals, you add the decimal places because each decimal place represents a power of 10. $ 0.01 $ has 2 places and $ 285.11 $ has 2 places, so the answer needs 2 + 2 = 4 places.

Q: Can I just ignore the decimals and multiply normally?

Yes! Multiply the numbers as if they were whole numbers first: 1 × 28511 = 28511. Then place the decimal point based on your total decimal place count.

Q: What if my answer has fewer digits than decimal places needed?

Add leading zeros as needed! If you need 4 decimal places but only have 3 digits, write it as 0.2851 instead of .2851 to make it clear.

Q: How can I check if 2.8511 is reasonable?

Estimate first: $ 0.01 \times 285 $ is about $ \frac{285}{100} = 2.85 $. Since 2.8511 is very close to 2.85, our answer makes sense!

Q: Why isn't the answer 28.511 like some of the choices?

That's a common mistake! 28.511 would mean we only moved the decimal 2 places instead of 4. Remember: total decimal places = 2 + 2 = 4 places from the right.

Decimal Multiplication with Place Value Counting

$0.01\times285.11=$

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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

00:10 There are 2 zeros in the denominator, so we'll move the decimal point twice

00:24 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

$0.01\times285.11=$

Step-by-step solution

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

Step 1: Multiply $0.01$ by $285.11$ considering decimal multiplication rules.
Step 2: Determine the placement of the decimal point in the product.
Step 3: Identify the correct answer choice based on the calculation.

Now, let's work through each step:

Step 1: First, convert the numbers into whole numbers and multiply:

$0.01 = \frac{1}{100}$ and $285.11 = 28511/100$ .

Ignoring the decimals temporarily, calculate $1 \times 28511 = 28511$ .

Step 2: Determine the placement of the decimal point:

Since $0.01$ has 2 decimal places and $285.11$ has 2 decimal places, the total number of decimal places in the product is $2 + 2 = 4$ .

Adjust the product $28511$ by placing the decimal point 4 places from the end:

This gives us $2.8511$ .

Step 3: Compare this result with the given choices.

The correct answer is the choice that matches our calculation:

The solution to the problem is $2.8511$ .

Final Answer

$2.8511$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total decimal places in both factors
Technique: 0.01 (2 places) × 285.11 (2 places) = 4 total places
Check: Product 28511 becomes 2.8511 with decimal 4 places from right ✓

Common Mistakes

Avoid these frequent errors

Placing the decimal point in the wrong position
Don't count decimal places separately for each number = wrong placement! This gives answers like 28.511 instead of 2.8511. Always add the total decimal places from both factors 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 together?

When multiplying decimals, you add the decimal places because each decimal place represents a power of 10. $0.01$ has 2 places and $285.11$ has 2 places, so the answer needs 2 + 2 = 4 places.

Can I just ignore the decimals and multiply normally?

Yes! Multiply the numbers as if they were whole numbers first: 1 × 28511 = 28511. Then place the decimal point based on your total decimal place count.

What if my answer has fewer digits than decimal places needed?

Add leading zeros as needed! If you need 4 decimal places but only have 3 digits, write it as 0.2851 instead of .2851 to make it clear.

How can I check if 2.8511 is reasonable?

Estimate first: $0.01 \times 285$ is about $\frac{285}{100} = 2.85$ . Since 2.8511 is very close to 2.85, our answer makes sense!

Why isn't the answer 28.511 like some of the choices?

That's a common mistake! 28.511 would mean we only moved the decimal 2 places instead of 4. Remember: total decimal places = 2 + 2 = 4 places from the right.

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