Decimal Multiplication: Place the Decimal Point in 0.3 × 2.15 = 0645

Q: How do I count decimal places correctly?

Count digits to the right of the decimal point in each number. In $ 0.3 $, there's 1 place (the 3). In $ 2.15 $, there are 2 places (the 1 and 5).

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

Start from the right side of your answer digits and count left! With 0645, count 3 places from right: 0-6-4-5 becomes 0.645.

Q: Why can't the answer be 6.45 or 64.5?

Think about reasonableness! You're multiplying 0.3 (less than 1) by 2.15, so your answer must be smaller than 2.15. Only 0.645 makes sense!

Q: What happens if I multiply the numbers without decimals first?

That's actually a great strategy! Multiply $ 3 \times 215 = 645 $, then place the decimal to get 3 total places: 0.645.

Q: Do I need to worry about the leading zero?

The leading zero in 0.645 is important for clarity! It shows that your answer is less than 1, which helps you check if your decimal placement makes sense.

Decimal Placement with Multiplication Counting

Look at the following exercise and work out the correct place of the decimal point in the answer:

$0.3\times2.15=0645$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place the decimal point

00:06 In the first factor there is one digit after the decimal point

00:11 And in the second factor there are 2 digits after the decimal point

00:16 Therefore we'll count 3 digits and then place the decimal point

00:21 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

Look at the following exercise and work out the correct place of the decimal point in the answer:

$0.3\times2.15=0645$

Step-by-step solution

In the number -0.3, there is one digit after the decimal point: 3.

In the number 2.15, there are two digits after the decimal point: 15.

Therefore, we have three digits after the decimal point.

To find the answer, we will count three decimal places to the left, which gives us -0.645.

Final Answer

$0.645$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total decimal places in both factors to place decimal
Technique: 0.3 (1 place) × 2.15 (2 places) = 3 total places
Check: Verify 0.3 × 2.15 = 0.645 gives reasonable size ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all decimal places
Don't just look at one number or guess where the decimal goes = wrong answer like 6.45 or 64.5! Missing decimal places makes your answer 10 or 100 times too big or small. Always count decimal places 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

How do I count decimal places correctly?

Count digits to the right of the decimal point in each number. In $0.3$ , there's 1 place (the 3). In $2.15$ , there are 2 places (the 1 and 5).

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

Start from the right side of your answer digits and count left! With 0645, count 3 places from right: 0-6-4-5 becomes 0.645.

Why can't the answer be 6.45 or 64.5?

Think about reasonableness! You're multiplying 0.3 (less than 1) by 2.15, so your answer must be smaller than 2.15. Only 0.645 makes sense!

What happens if I multiply the numbers without decimals first?

That's actually a great strategy! Multiply $3 \times 215 = 645$ , then place the decimal to get 3 total places: 0.645.

Do I need to worry about the leading zero?

The leading zero in 0.645 is important for clarity! It shows that your answer is less than 1, which helps you check if your decimal placement makes sense.

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