Solve Decimal Division: 0.1 ÷ 0.02 Step-by-Step Solution

Decimal Division with Converting to Whole Numbers

0.1:0.02= 0.1:0.02=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together!
00:09 First, multiply each number by one hundred. This makes it easier to divide.
00:30 Now, divide these new numbers to find the answer.
00:36 And that's how we solve the question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0.1:0.02= 0.1:0.02=

2

Step-by-step solution

To solve the problem 0.1÷0.020.1 \div 0.02, let's follow these steps:

  • Step 1: Eliminate the decimals by multiplying both the dividend and divisor by 100 to convert them to whole numbers.
  • Step 2: Convert 0.10.1 to 1010 and 0.020.02 to 22 by multiplication.
  • Step 3: Perform the division 10÷210 \div 2.

Now, let's proceed with the calculations:
- When we multiply 0.10.1 by 100, we get 1010. Similarly, multiplying 0.020.02 by 100 gives us 22.
- Next, we divide 1010 by 22:
10÷2=510 \div 2 = 5.

Therefore, the solution to the problem is 5 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply both dividend and divisor by same power of 10
  • Technique: Convert 0.1 ÷ 0.02 to 10 ÷ 2 by multiplying by 100
  • Check: Verify 5 × 0.02 = 0.1 ✓

Common Mistakes

Avoid these frequent errors
  • Multiplying dividend and divisor by different powers of 10
    Don't multiply 0.1 by 10 and 0.02 by 100 = 1 ÷ 2 = 0.5 instead of 5! This changes the ratio and gives wrong answers. Always multiply both numbers by the same power of 10 to eliminate all decimals.

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 we multiply both numbers by the same value?

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When you multiply both the dividend and divisor by the same number, you're not changing the answer! It's like having 12 \frac{1}{2} and 1020 \frac{10}{20} - they're equal because you multiplied top and bottom by 10.

How do I know what power of 10 to use?

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Look at the number with more decimal places. Since 0.02 has 2 decimal places, multiply both numbers by 102=100 10^2 = 100 to eliminate all decimals.

Can I just move the decimal points instead?

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Yes! Moving decimal points is the same as multiplying by powers of 10. Move both decimal points the same number of places to the right until all decimals disappear.

What if I get confused about which direction to move decimals?

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Think of it as making both numbers bigger by the same amount. Moving decimals to the right makes numbers larger: 0.1 becomes 1, then 10.

How can I check if my answer is right?

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Use multiplication! If 0.1÷0.02=5 0.1 ÷ 0.02 = 5 , then 5×0.02 5 × 0.02 should equal 0.1 0.1 . Indeed: 5×0.02=0.10=0.1 5 × 0.02 = 0.10 = 0.1

Is there an easier way than converting to whole numbers?

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You could use long division with decimals, but converting to whole numbers usually makes the math much simpler and reduces errors!

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