Q1. Which fraction has a terminating decimal expansion?
✔ Denominator 4 is 2^2, which fits the rule for terminating decimals.
Q2. What determines the type of decimal expansion?
✔ Only the prime factors of the simplified denominator matter.
Q3. Simplify 6/12 before checking. What is q?
✔ 6/12 reduces to 1/2, so the denominator q is 2.
Show transcript
[Slide 1] What is a Decimal Expansion?
Welcome students. Today we learn about decimal expansions of rational numbers. A rational number is any fraction where p and q are integers. Its decimal form either stops or repeats infinitely.
[Slide 2] The Prime Factorization Rule
To find the type, simplify your fraction first. Look at the prime factors of the denominator q. If q equals two to the power m times five to the power n, it terminates.
[Slide 3] Solving a Real Problem
Let us take the number seven by twenty. The denominator twenty factors into two squared times five one. Since it only has twos and fives, the decimal stops.
[Slide 4] Avoid This Common Error
Many students check the denominator without simplifying. Remember, only the simplified denominator matters for the rule. The numerator does not affect whether it terminates or repeats.
[Slide 5] Key Takeaways Summary
In summary, always simplify your rational number first. Check the prime factors of the denominator alone. This simple rule guarantees full marks in your board exam.
[Slide 6] Board Exam Strategy
For your boards, practice prime factorization quickly. Knowing powers of two and five helps speed up solving. Manage your time wisely during the exam paper.