Multiply 4.16 × 100: Decimal Place Value Shift

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

Multiplying by 100 is like multiplying by 10 twice. Each multiplication by 10 moves the decimal one place right, so 100 moves it two places right.

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

Add zeros to fill the empty places! For example, if you multiply 2.5 × 100, you get 250 (the zero fills the empty place).

Q: How do I remember which direction to move the decimal?

Think about size: multiplication makes numbers bigger, so the decimal moves right (toward bigger place values). Division makes numbers smaller, so decimal moves left.

Q: What if my answer doesn't match any of the choices?

Double-check that you moved the decimal the correct number of places and in the right direction. Count the zeros in your multiplier carefully!

Decimal Multiplication with Powers of Ten

$4.16\times100=$

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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

00:07 Move the decimal point according to the number of 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

$4.16\times100=$

Step-by-step solution

To solve the problem of multiplying $4.16$ by $100$ , we follow specific steps:

Step 1: Identify the Original Position of the Decimal
The number $4.16$ has a decimal point between the 4 and the 1, giving it two decimal places.
Step 2: Apply the Multiplication Operation
Multiplying by $100$ involves moving the decimal point two places to the right because $100$ has two zeros.
Step 3: Shift the Decimal Point
By shifting the decimal point two places to the right, $4.16$ becomes $416.$
Step 4: Verify Against Answer Choices
$416$ matches choice number 2 in the given multiple-choice list.

Therefore, the solution to the problem is $416$ .

Final Answer

$416$

Key Points to Remember

Essential concepts to master this topic

Rule: When multiplying by 100, move decimal point two places right
Technique: Count zeros in multiplier: 100 has two zeros = move 2 places
Check: Verify $4.16 \times 100 = 416$ by dividing 416 ÷ 100 = 4.16 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction or wrong number of places
Don't move the decimal left or only one place = wrong answer like 41.6 or 0.416! Moving left makes numbers smaller, but multiplication should make them larger. Always move decimal point right the same number of places as zeros in the power of ten.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why does multiplying by 100 move the decimal point?

Multiplying by 100 is like multiplying by 10 twice. Each multiplication by 10 moves the decimal one place right, so 100 moves it two places right.

What if there aren't enough digits to move the decimal?

Add zeros to fill the empty places! For example, if you multiply 2.5 × 100, you get 250 (the zero fills the empty place).

Does this work for other powers of 10 like 1000?

Yes! The pattern is simple:

10 = 1 zero → move 1 place right
100 = 2 zeros → move 2 places right
1000 = 3 zeros → move 3 places right

How do I remember which direction to move the decimal?

Think about size: multiplication makes numbers bigger, so the decimal moves right (toward bigger place values). Division makes numbers smaller, so decimal moves left.

What if my answer doesn't match any of the choices?

Double-check that you moved the decimal the correct number of places and in the right direction. Count the zeros in your multiplier carefully!

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