Solve Decimal Division: 0.4 ÷ 0.2 Step-by-Step

Q: Why do we multiply both numbers by 10?

Multiplying both the dividend (0.4) and divisor (0.2) by 10 keeps the division equal while making it easier to solve. It's like having $ \frac{0.4}{0.2} = \frac{4}{2} $!

Q: What if the decimals have different numbers of decimal places?

Use the number with more decimal places to decide your multiplier. For example, if you have 0.25 ÷ 0.5, multiply both by 100 to get $ 25 ÷ 50 $.

Q: Can I just remove the decimal points?

No! You must multiply by the same power of 10, not just erase decimals. Removing decimal points from 0.4 ÷ 0.2 would incorrectly give you $ 4 ÷ 2 $, which happens to work here but fails with different problems.

Q: How do I know what power of 10 to use?

Count the maximum number of decimal places in either number. Here both 0.4 and 0.2 have 1 decimal place, so multiply by $ 10^1 = 10 $.

Q: Is there another way to solve this?

Yes! You can think of it as "How many 0.2s fit into 0.4?" Since 0.2 + 0.2 = 0.4, exactly 2 of them fit, so the answer is 2.

Decimal Division with Equivalent Multiplication

$0.4:0.2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Multiply each factor by 10, to make it easier to divide

00:22 Divide between the new numbers, and calculate the quotient

00:26 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

$0.4:0.2=$

Step-by-step solution

To solve the problem $0.4 \div 0.2$ , we can follow these steps:

Step 1: Convert the division of decimals into a division of whole numbers by multiplying both the dividend (0.4) and the divisor (0.2) by 10.
Step 2: This operation results in dividing 4 by 2 (since $0.4 \times 10 = 4$ and $0.2 \times 10 = 2$ ).
Step 3: Perform the division $4 \div 2$ , which equals 2.

Thus, the result of dividing $0.4$ by $0.2$ is $\boxed{2}$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numbers by same power of 10 to eliminate decimals
Technique: Convert $0.4 \div 0.2$ to $4 \div 2$ by multiplying by 10
Check: Verify $2 \times 0.2 = 0.4$ confirms our answer is correct ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply both dividend and divisor by the same number
Don't multiply only 0.4 by 10 to get 4 ÷ 0.2 = 20! This changes the problem completely and gives a wrong answer. Always multiply both the dividend AND divisor by the same power of 10 to keep the division equivalent.

Practice Quiz

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Solve the following exercise:

FAQ

Everything you need to know about this question

Why do we multiply both numbers by 10?

Multiplying both the dividend (0.4) and divisor (0.2) by 10 keeps the division equal while making it easier to solve. It's like having $\frac{0.4}{0.2} = \frac{4}{2}$ !

What if the decimals have different numbers of decimal places?

Use the number with more decimal places to decide your multiplier. For example, if you have 0.25 ÷ 0.5, multiply both by 100 to get $25 ÷ 50$ .

Can I just remove the decimal points?

No! You must multiply by the same power of 10, not just erase decimals. Removing decimal points from 0.4 ÷ 0.2 would incorrectly give you $4 ÷ 2$ , which happens to work here but fails with different problems.

How do I know what power of 10 to use?

Count the maximum number of decimal places in either number. Here both 0.4 and 0.2 have 1 decimal place, so multiply by $10^1 = 10$ .

Is there another way to solve this?

Yes! You can think of it as "How many 0.2s fit into 0.4?" Since 0.2 + 0.2 = 0.4, exactly 2 of them fit, so the answer is 2.

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Solve Decimal Division: 0.4 ÷ 0.2 Step-by-Step

Decimal Division with Equivalent Multiplication

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we multiply both numbers by 10?

What if the decimals have different numbers of decimal places?

Can I just remove the decimal points?

How do I know what power of 10 to use?

Is there another way to solve this?

🌟 Unlock Your Math Potential

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