Solve Decimal Division: 10.9 ÷ 2.5 Step-by-Step

Decimal Division with Place Value Conversion

10.9:2.5= 10.9:2.5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Write each number as a whole number, and divide
00:13 Break down the fraction into whole fraction and remainder
00:27 Convert whole fraction to whole number
00:36 Multiply by the appropriate whole fraction, so the denominator becomes 100
00:52 Convert decimal fraction to decimal number
00:56 Add to decimal number
01:00 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

10.9:2.5= 10.9:2.5=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the problem to integer division.
  • Step 2: Perform the division.
  • Step 3: Adjust for decimal placement.

Now, let's work through each step:

Step 1: Convert the problem to integer division.
Multiply both 10.9 and 2.5 by 10 to eliminate the decimals, yielding 109 and 25, respectively.

Step 2: Perform the division.
Divide 109 by 25. When dividing, you get 4 as the quotient and a remainder of 9. Therefore, 109 ÷ 25 = 4.36.

Step 3: Adjust for decimal placement.
Since we initially multiplied by 10, dividing by 25 effectively places the decimal in the correct position. Thus, 10.9 ÷ 2.5 = 4.36.

Therefore, the solution to the problem is 4.36 4.36 .

3

Final Answer

4.36 4.36

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply both numbers by same power of 10 to eliminate decimals
  • Technique: 10.9×10=109 10.9 \times 10 = 109 and 2.5×10=25 2.5 \times 10 = 25 , then divide
  • Check: Multiply answer by divisor: 4.36×2.5=10.9 4.36 \times 2.5 = 10.9

Common Mistakes

Avoid these frequent errors
  • Not multiplying both numbers by the same power of 10
    Don't multiply only one decimal by 10 while leaving the other unchanged = wrong decimal placement! This shifts the decimal point incorrectly and gives a completely wrong answer. Always multiply both the dividend and divisor by the same power of 10 to maintain the correct ratio.

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 I multiply both numbers by 10?

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Multiplying both numbers by the same amount keeps the division equal! Think of it like this: 10.92.5=10925 \frac{10.9}{2.5} = \frac{109}{25} - the ratio stays the same, but now you're dividing whole numbers.

How do I know which power of 10 to use?

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Count the maximum decimal places in either number. Here, both 10.9 and 2.5 have 1 decimal place, so multiply by 101=10 10^1 = 10 . If one had 2 decimal places, you'd use 100.

What if my division doesn't come out evenly?

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That's normal! Continue dividing to get more decimal places, or round to the required precision. In this problem, 109÷25=4.36 109 \div 25 = 4.36 exactly.

Can I just move decimal points instead?

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Yes! Moving the decimal point right is the same as multiplying by 10. Just remember to move it the same number of places in both numbers: 10.9 → 109 and 2.5 → 25.

How do I check if 4.36 is really correct?

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Multiply your answer by the original divisor: 4.36×2.5 4.36 \times 2.5 . If you get 10.9, you're right! This backwards check always works for division problems.

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