Solve Decimal Multiplication: 37.1 × 100 Step-by-Step

Q: Why does multiplying by 100 move the decimal point?

Think of 100 as 10²! Each factor of 10 moves the decimal one place right. Since 100 = 10 × 10, you move the decimal two places right.

Q: What if there aren't enough digits after the decimal?

Just add zeros! For example, 37.1 × 100: move right twice to get 3710. The missing digit becomes a zero automatically.

Q: Does this work for other powers of 10?

Yes! Count the zeros: 10 (one zero) = move 1 place, 1000 (three zeros) = move 3 places, and so on.

Q: What about multiplying by 0.1 or 0.01?

These move the decimal left! Since 0.1 = 1/10, you're dividing by 10, so $ 37.1 \times 0.1 = 3.71 $.

Q: How do I remember which direction to move?

Bigger multiplier = bigger answer! Since 100 > 1, your answer should be bigger than 37.1, so move decimal right to make it bigger.

Decimal Multiplication with Powers of Ten

$37.1\times100=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the number of zeros, move the decimal point

00:10 Move the decimal point by 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

Understand the problem

$37.1\times100=$

Step-by-step solution

To solve the problem of multiplying $37.1$ by $100$ , we can follow these steps:

Step 1: Understand that multiplying by 100 involves moving the decimal point two places to the right.
Step 2: Begin with the number $37.1$ .
Step 3: Move the decimal point two places to the right.

Now, let's perform the operation:
- The original number is $37.1$ .
- When we move the decimal point two places to the right, $37.1$ becomes $3710.0$ .
- For clarity, $3710.0$ is the same as $3710$ , as the .0 does not change the value.

Thus, the result of multiplying $37.1 \times 100$ is $3710$ .

Final Answer

$3710$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplying by 100 moves decimal point two places right
Technique: From 37.1, move decimal right twice: 37.1 → 371.0 → 3710
Check: Count zeros in 100 (two) equals decimal places moved (two) ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction
Don't move the decimal point left when multiplying by 100 = 0.371 instead of 3710! Moving left makes numbers smaller, but multiplying should make them bigger. Always move the decimal point right when multiplying by powers of 10.

Practice Quiz

Test your knowledge with interactive questions

$$ 20.1:10= $$

FAQ

Everything you need to know about this question

Why does multiplying by 100 move the decimal point?

Think of 100 as 10²! Each factor of 10 moves the decimal one place right. Since 100 = 10 × 10, you move the decimal two places right.

What if there aren't enough digits after the decimal?

Just add zeros! For example, 37.1 × 100: move right twice to get 3710. The missing digit becomes a zero automatically.

Does this work for other powers of 10?

Yes! Count the zeros: 10 (one zero) = move 1 place, 1000 (three zeros) = move 3 places, and so on.

What about multiplying by 0.1 or 0.01?

These move the decimal left! Since 0.1 = 1/10, you're dividing by 10, so $37.1 \times 0.1 = 3.71$ .

How do I remember which direction to move?

Bigger multiplier = bigger answer! Since 100 > 1, your answer should be bigger than 37.1, so move decimal right to make it bigger.

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