Notes on Dividing Decimals by Decimals

Introduction

• The lecture covers how to divide a decimal by a decimal.
• Two examples are provided to illustrate the process.

Example 1: Dividing 5.76 by 0.3

1. Setup
   • Dividend: 5.76 (goes under the division bar).
   • Divisor: 0.3 (goes outside the division bar).
2. Is the Divisor a Whole Number?
   • No, 0.3 is not a whole number.
   • Convert to a whole number by multiplying by a power of 10 (move the decimal right).
   • 0.3 becomes 3 (multiply by 10).
3. Adjust the Dividend
   • Similarly, multiply 5.76 by 10 to adjust.
   • Resulting dividend: 57.6.
4. Division Process
   • Move the decimal straight up in the quotient.
   • Follow standard division steps:
     • 5 divided by 3 = 1, remainder 2.
     • Bring down 7, 27 divided by 3 = 9, remainder 0.
     • Bring down 6, 6 divided by 3 = 2, remainder 0.
   • Final answer: 19.2.

Example 2: Dividing 86.4 by 0.12

1. Setup
   • Dividend: 86.4.
   • Divisor: 0.12.
2. Is the Divisor a Whole Number?
   • No, need to multiply by 100 to shift decimal twice.
   • 0.12 becomes 12.
3. Adjust the Dividend
   • Multiply 86.4 by 100.
   • Resulting dividend: 8640.
4. Division Process
   • Move decimal point and set up division.
   • 8 divided by 12 = 0, use 86 instead.
   • 86 divided by 12 = 7, remainder 2.
   • Bring down 4, 24 divided by 12 = 2, remainder 0.
   • Bring down 0, 0 divided by 12 = 0.
   • Final answer: 720.

Key Points

• Convert Divisor to a Whole Number: Use powers of 10.
• Adjust Dividend Similarly: Apply the same power of 10.
• Division Steps: Standard division process with decimal adjustment.
• Result Verification: Ensure step-by-step accuracy for the correct answer.

Conclusion

• Check if the divisor is a whole number.
• Adjust both divisor and dividend using powers of 10.
• Follow the division process meticulously for accuracy.

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This method ensures accurate division of decimals and avoids common pitfalls associated with decimal placement in division problems.