Among (\frac{1}{6}), (\frac{1}{12}), (\frac{1}{15}), and (\frac{1}{30}), which has the shortest terminating part before the recurring part starts?
Answer and explanation
Correct answer: (\frac{1}{6})
Step 1: A denominator with (3) along with (2) or (5) gives a non-terminating recurring decimal. Step 2: (\frac{1}{6}=\frac{1}{2\cdot 3}), so the recurring part starts earliest. The others have (2^2), (5), or (2\cdot 5), causing a longer non-repeating start. Step 3: In mixed denominators, powers of (2) and (5) show how much the recurring part is delayed.
Frequently asked questions
What is the correct answer to this question?
(\frac{1}{6})
Why is this the correct answer?
Step 1: A denominator with (3) along with (2) or (5) gives a non-terminating recurring decimal. Step 2: (\frac{1}{6}=\frac{1}{2\cdot 3}), so the recurring part starts earliest. The others have (2^2), (5), or (2\cdot 5), causing a longer non-repeating start. Step 3: In mixed denominators, powers of (2) and (5) show how much the recurring part is delayed.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.
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