Arithmetic: Dividing Decimals Completely

Dividing decimals follows the same principles as whole-number division but requires careful attention to decimal placement. The goal is to ensure the division process results in a complete quotient, sometimes requiring rounding or adding trailing zeros.

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Types of Decimal Division

1. Dividing a decimal by a whole number (e.g., 24.6 ÷ 3)
2. Dividing a decimal by another decimal (e.g., 3.75 ÷ 1.5)
3. Ensuring a complete quotient (sometimes requiring extra decimal places)

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Case 1: Dividing a Decimal by a Whole Number

Example: 37.8 ÷ 6

Step 1: Set Up the Long Division

Step 2: Divide as Usual

• 37 ÷ 6 = 6 (since 6 × 6 = 36)
• Subtract: 37 - 36 = 1
• Bring down the 8 → New number is 18
• 18 ÷ 6 = 3 (since 6 × 3 = 18)

Step 3: Place the Decimal in the Quotient

• The decimal in 37.8 aligns directly above in the answer.
• The final quotient is 6.3

✅ Final Answer: 6.3

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Case 2: Dividing a Decimal by Another Decimal

Example: 5.4 ÷ 0.9

Step 1: Make the Divisor a Whole Number

Move the decimal in 0.9 one place right → It becomes 9.
Do the same for 5.4, making it 54.

Now, solve:

✅ Final Answer: 6

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Case 3: Ensuring a Complete Quotient

Example: 4 ÷ 0.8

Step 1: Convert the Divisor into a Whole Number

Move the decimal one place → 0.8 → 8
Do the same for 4, making it 40.

Now, solve:

 

✅ Final Answer: 5

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Case 4: When the Division Doesn’t End (Repeating Decimals)

Example: 7 ÷ 3

Step 1: Divide as Usual

• 7 ÷ 3 = 2 (remainder 1)
• Add a decimal and a 0 → New number is 10
• 10 ÷ 3 = 3 (remainder 1)
• Another 0 → New number is 10
• 10 ÷ 3 = 3 again… (keeps repeating)

Step 2: Identify the Pattern

• The quotient is 2.333…, meaning 2.3̅ (repeating decimal).

✅ Final Answer: 2.3̅ (or rounded to 2.33 if needed)

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Practice Problems

1. 42.5 ÷ 5
2. 9.6 ÷ 0.4
3. 15.75 ÷ 2.5
4. 8.4 ÷ 3
5. 11 ÷ 4 (Write as a repeating decimal)

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