Solve Decimal Multiplication: 0.01 × 0.45 Step-by-Step

Q: Why do I need to count decimal places?

Counting decimal places ensures your answer has the correct size! When you multiply decimals, the product becomes smaller, so you need more decimal places than either original number.

Q: What if I forget where to put the decimal point?

Use this trick: multiply the numbers as if they were whole numbers first, then count the total decimal places in both original numbers and move the decimal that many places from the right.

Q: Can I convert to fractions instead?

Yes! $ 0.01 = \frac{1}{100} $ and $ 0.45 = \frac{45}{100} $. Multiply fractions: $ \frac{1 \times 45}{100 \times 100} = \frac{45}{10000} = 0.0045 $

Q: How do I know if 0.0045 makes sense?

Use estimation! $ 0.01 \times 0.45 $ is about $ 0.01 \times 0.5 = 0.005 $, so 0.0045 is reasonable since it's close to 0.005.

Q: What's the difference between 0.0045 and 0.045?

They differ by a factor of 10! $ 0.045 = 10 \times 0.0045 $. This is why precise decimal placement is crucial - one wrong position changes your answer dramatically.

Decimal Multiplication with Place Value Management

$\text{0}.01\times0.45=$

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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

00:11 There are 2 zeros in the denominator, so we'll add 2 zeros

00:15 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

$\text{0}.01\times0.45=$

Step-by-step solution

To solve this multiplication problem, we will follow these steps:

Step 1: Convert both decimal numbers to fractions or remove the decimals by considering them as whole numbers.
Step 2: Multiply these whole numbers.
Step 3: Place the decimal in the resulting product correctly by counting the sum of the decimal places in the original numbers.

Now, let's work through each step:

Step 1: We have the numbers $0.01$ and $0.45$ .
Convert $0.01$ to $\frac{1}{100}$ and $0.45$ to $\frac{45}{100}$ .

Step 2: Multiply $\frac{1}{100} \times \frac{45}{100} = \frac{1 \times 45}{100 \times 100} = \frac{45}{10000}$ .

Step 3: Convert $\frac{45}{10000}$ back to a decimal form. Since $10000$ has 4 zeros, move the decimal four places to the left: $0.0045$ .

Therefore, the product of $0.01$ and $0.45$ is $0.0045$ .

Final Answer

$0.0045$

Key Points to Remember

Essential concepts to master this topic

Rule: Total decimal places in product equals sum of decimal places
Technique: Multiply 1 × 45 = 45, then place decimal 4 positions left
Check: Count decimal places: 2 + 2 = 4 places gives 0.0045 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly counting decimal places
Don't count only some decimal places or forget zeros = wrong decimal placement! This puts the decimal in the wrong position, making answers 10 or 100 times too big or small. Always count every decimal place in both numbers and add them together.

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 need to count decimal places?

Counting decimal places ensures your answer has the correct size! When you multiply decimals, the product becomes smaller, so you need more decimal places than either original number.

What if I forget where to put the decimal point?

Use this trick: multiply the numbers as if they were whole numbers first, then count the total decimal places in both original numbers and move the decimal that many places from the right.

Can I convert to fractions instead?

Yes! $0.01 = \frac{1}{100}$ and $0.45 = \frac{45}{100}$ . Multiply fractions: $\frac{1 \times 45}{100 \times 100} = \frac{45}{10000} = 0.0045$

How do I know if 0.0045 makes sense?

Use estimation! $0.01 \times 0.45$ is about $0.01 \times 0.5 = 0.005$ , so 0.0045 is reasonable since it's close to 0.005.

What's the difference between 0.0045 and 0.045?

They differ by a factor of 10! $0.045 = 10 \times 0.0045$ . This is why precise decimal placement is crucial - one wrong position changes your answer dramatically.

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