Dividing Decimals (Set 4)

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Dividing Decimals (Set 4)

 

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Division with decimals follows the same fundamental concept as whole number division. The key difference is that we need to properly position the decimal point in our quotient (answer). The good news is that we can convert decimal division into whole number division using a simple technique.


Remember: Division is finding how many times one number (the divisor) goes into another number (the dividend) to get a result (the quotient).


Steps for Dividing Decimals


  1. Convert to a whole number division problem
    • Move the decimal point in the divisor to the right until it becomes a whole number
    • Move the decimal point in the dividend the same number of places to the right
    • This doesn't change the value of the division

  2. Perform standard long division
    • Divide as you would with whole numbers

  3. Place the decimal point in the quotient
    • The decimal point in the quotient goes directly above the decimal point in the dividend

  4. Check your answer
    • Multiply your answer by the divisor to verify it equals the dividend

Examples


Example 1: Dividing 8.4 ÷ 2


Step 1: The divisor is already a whole number, so no adjustment needed


Step 2: Perform long division

    4.2
  -----
2 ) 8.4
    8.0
    ---
    0.4
    0.4
    ---
    0.0

Therefore, 8.4 ÷ 2 = 4.2


Example 2: Dividing 12.6 ÷ 0.3


Step 1: Convert to a whole number division problem

  • Move the decimal point in the divisor 1 place right: 0.3 → 3
  • Move the decimal point in the dividend 1 place right: 12.6 → 126

Step 2: Perform long division

     42
   -----
 3 ) 126
     12
     ---
      06
      06
      --
       0

Therefore, 12.6 ÷ 0.3 = 42


Example 3: Dividing 5.25 ÷ 2.5


Step 1: Convert to a whole number division problem

  • Move the decimal point in the divisor 1 place right: 2.5 → 25
  • Move the decimal point in the dividend 1 place right: 5.25 → 52.5

Step 2: Perform long division

      2.1
    ------
 25 ) 52.5
      50.0
      ----
       2.5
       2.5
       ---
       0.0

Therefore, 5.25 ÷ 2.5 = 2.1


Example 4: Dividing 1.8 ÷ 0.15


Step 1: Convert to a whole number division problem

  • Move the decimal point in the divisor 2 places right: 0.15 → 15
  • Move the decimal point in the dividend 2 places right: 1.8 → 180

Step 2: Perform long division

      12
    -----
 15 ) 180
      15
      ---
       30
       30
       --
        0

Therefore, 1.8 ÷ 0.15 = 12


Special Cases


Dividing by Powers of 10


When dividing a decimal by 10, 100, 1000, etc., you can simply move the decimal point to the left by the number of zeros in the power of 10:

  • 235 ÷ 10 = 23.5 (move 1 place left)
  • 235 ÷ 100 = 2.35 (move 2 places left)
  • 235 ÷ 1000 = 0.235 (move 3 places left)

Division Resulting in Repeating Decimals


Some divisions result in decimals that repeat indefinitely. For example:

      0.333...
    ---------
 3 ) 1.000...
      0.9
      ---
       10
        9
      ---
       10
        9
      ---
       etc.

In this case, 1 ÷ 3 = 0.333... (the 3 repeats forever). We write this as 0.3̅ with a bar over the repeating digit.


Common Mistakes to Avoid


  • Incorrect decimal point placement: Always move the decimal points in both numbers the same number of places
  • Calculation errors: Carefully work through the long division process
  • Forgetting to add zeros: Sometimes you need to add zeros to the dividend to complete the division
  • Estimation oversight: Use estimation to verify if your answer is reasonable

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