Solve Decimal Division: 10.4 ÷ 5.2 Step-by-Step

Decimal Division with Equivalent Integer Conversion

10.4:5.2= 10.4:5.2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Let's multiply each factor by 10 to make it easier to divide
00:28 Let's divide between the new numbers and calculate the quotient
00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

10.4:5.2= 10.4:5.2=

2

Step-by-step solution

To solve this problem, we need to divide 10.410.4 by 5.25.2. We can achieve this by simplifying the division process:

  • Step 1: Eliminate decimals by multiplying both numbers by 10. Thus, we have 10.4×10=10410.4 \times 10 = 104 and 5.2×10=525.2 \times 10 = 52.
  • Step 2: Now, divide the resulting integers: 10452\frac{104}{52}.
  • Step 3: Perform the division: 104÷52=2104 \div 52 = 2.

Thus, the result of dividing 10.410.4 by 5.25.2 is 2\mathbf{2}.

3

Final Answer

2 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 10.4÷5.2 10.4 \div 5.2 to 104÷52 104 \div 52 by multiplying by 10
  • Check: Verify 5.2×2=10.4 5.2 \times 2 = 10.4 confirms our answer is correct ✓

Common Mistakes

Avoid these frequent errors
  • Moving decimal points different amounts in dividend and divisor
    Don't move the decimal 1 place in 10.4 but 2 places in 5.2 = creates unequal scaling! This changes the actual value of the division. Always multiply both numbers by the exact same power of 10.

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 can I multiply both numbers by 10 without changing the answer?

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Because division follows the scaling property! When you multiply both the dividend and divisor by the same number, the quotient stays identical. It's like having 2010=4020=2 \frac{20}{10} = \frac{40}{20} = 2 .

What if the decimals have different numbers of decimal places?

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Multiply by the power of 10 needed for the number with more decimal places. For example, if you have 12.45 ÷ 3.2, multiply both by 100 to get 1245 ÷ 320.

Can I just ignore the decimal points and divide normally?

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No! You must account for decimal placement. Always use the proper method of multiplying both numbers by the same power of 10, or you'll get the wrong answer.

How do I know what power of 10 to use?

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Count the decimal places in each number and use the power of 10 that eliminates all decimals. One decimal place = ×10, two decimal places = ×100, etc.

What if my answer doesn't come out to a whole number?

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That's totally normal! Many decimal divisions result in decimals or fractions. Just make sure to show your work clearly and double-check by multiplying back.

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