Solve Division Problem: 0.4 Divided by 200

Q: How do I convert 0.4 to a fraction?

Look at the decimal place: 0.4 has one decimal place, so it equals $\frac{4}{10}$. The denominator is always a power of 10 based on decimal places!

Q: Why do I multiply by the reciprocal when dividing fractions?

Division by a number is the same as multiplication by its reciprocal. So $\div 200$ becomes $\times \frac{1}{200}$, making the calculation easier!

Q: How can I check if 0.002 is correct?

Use inverse operations! Since $0.4 \div 200 = 0.002$, then $0.002 \times 200$ should equal $0.4$. Try it: $0.002 \times 200 = 0.4$ ✓

Q: What's the easiest way to multiply fractions like this?

Multiply straight across: $\frac{4}{10} \times \frac{1}{200} = \frac{4 \times 1}{10 \times 200} = \frac{4}{2000}$. Then simplify by dividing both parts by their greatest common factor!

Decimal Division with Large Denominators

$0.4:200=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:08 First, convert the division into a fraction.

00:12 Now, reduce the fraction as much as possible.

00:21 Look at the zeros in the denominator. Move the decimal point accordingly.

00:32 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$0.4:200=$

Step-by-step solution

To solve the problem of dividing $0.4$ by $200$ , we can follow the steps outlined below:

Step 1: Convert the decimal to a fraction.
$0.4$ is equivalent to $\frac{4}{10}$ .
Step 2: Set up the division as a fraction.
The division $0.4 \div 200$ can be rewritten as $\frac{4}{10} \div 200$ . This is the same as multiplying by the reciprocal of $200$ , thus $\frac{4}{10} \times \frac{1}{200}$ .
Step 3: Simplify the fraction.
Multiply the fractions: $\frac{4 \times 1}{10 \times 200} = \frac{4}{2000}$ .
Step 4: Simplify further if possible.
Divide the numerator and denominator by the greatest common factor. The greatest common factor of 4 and 2000 is 4.
Thus, $\frac{4}{2000} = \frac{1}{500}$ .
Step 5: Convert the simplified fraction back to a decimal.
The fraction $\frac{1}{500}$ in decimal form is $0.002$ .

Therefore, the solution to the problem is $0.002$ .

Final Answer

$0.002$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimals to fractions when dividing by large numbers
Technique: Transform $0.4 \div 200$ into $\frac{4}{10} \times \frac{1}{200}$
Check: Verify $0.002 \times 200 = 0.4$ by multiplication ✓

Common Mistakes

Avoid these frequent errors

Treating division like simple place value shifts
Don't just move the decimal point left three places because 200 has two zeros = wrong answer of 0.0004! This ignores the actual mathematical relationship. Always convert to fractions or use proper long division when dividing decimals by large numbers.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just move the decimal point when dividing by 200?

Moving decimal points works for powers of 10 (like 10, 100, 1000), but 200 is not a power of 10! You must actually divide: $0.4 \div 200 = 0.002$ , not just shift places.

How do I convert 0.4 to a fraction?

Look at the decimal place: 0.4 has one decimal place, so it equals $\frac{4}{10}$ . The denominator is always a power of 10 based on decimal places!

Why do I multiply by the reciprocal when dividing fractions?

Division by a number is the same as multiplication by its reciprocal. So $\div 200$ becomes $\times \frac{1}{200}$ , making the calculation easier!

How can I check if 0.002 is correct?

Use inverse operations! Since $0.4 \div 200 = 0.002$ , then $0.002 \times 200$ should equal $0.4$ . Try it: $0.002 \times 200 = 0.4$ ✓

What's the easiest way to multiply fractions like this?

Multiply straight across: $\frac{4}{10} \times \frac{1}{200} = \frac{4 \times 1}{10 \times 200} = \frac{4}{2000}$ . Then simplify by dividing both parts by their greatest common factor!

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