Solve: 3.412 × 100 - Decimal Multiplication with Powers of Ten

Decimal Multiplication with Powers of Ten

3.412×100= 3.412\times100=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 According to the number of zeros, move the decimal point
00:14 Move the point according to the number of zeros
00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3.412×100= 3.412\times100=

2

Step-by-step solution

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

  • Step 1: Identify the original position of the decimal point in 3.412.
  • Step 2: Shift the decimal point two places to the right because we are multiplying by 100.
  • Step 3: Write down the new number after shifting the decimal point.

Now, let's perform the solution:
Step 1: In the number 3.412, the decimal point is initially between the 3 and the 4.
Step 2: We shift this decimal point two places to the right, which changes the value to 341.2.
Step 3: The resulting number after this operation is 341.2.

Therefore, the solution to the problem is 341.2 341.2 .

3

Final Answer

341.2 341.2

Key Points to Remember

Essential concepts to master this topic
  • Rule: When multiplying by 100, move decimal point two places right
  • Technique: From 3.412, move decimal right twice: 3.4→34.1→341.2
  • Check: Count decimal places: 3 places becomes 1 place (3-2=1) ✓

Common Mistakes

Avoid these frequent errors
  • Moving decimal point the wrong direction
    Don't move the decimal point left when multiplying by 100 = gives 0.03412! This makes the number smaller instead of larger. Always move the decimal point right when multiplying by powers of ten.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

22.1-12.0

FAQ

Everything you need to know about this question

Why do I move the decimal point right when multiplying by 100?

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Because multiplying makes numbers larger! Moving the decimal right increases the value. Remember: multiply = move right, divide = move left.

How many places do I move for different powers of ten?

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Count the zeros! For 10 (1 zero) = 1 place, for 100 (2 zeros) = 2 places, for 1000 (3 zeros) = 3 places.

What if I don't have enough digits to move the decimal?

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Add zeros as placeholders! For example: 2.5×1000=2500 2.5 \times 1000 = 2500 (added two zeros).

Does this work for any decimal number?

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Yes! This shortcut works for any decimal multiplied by powers of ten (10, 100, 1000, etc.). It's much faster than regular multiplication!

How can I remember which direction to move?

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Think: "Bigger number, bigger place!" When multiplying (making bigger), move decimal to make a bigger-looking number by going right.

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