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Two tankers contain 850 litres and 680 litres of petrol. Find the maximum capacity of a container that can measure the petrol of each tanker an exact number of times.

Class 10Real NumbersNumber Systems
  • A340
  • B170
  • C185
  • D155

Step-by-Step Solution

Maximum capacity = HCF(850, 680). 850 = 2··5·17. HCF = 2·5·17 = 170 litres.
Answer: B) 170

Key idea: When does a rational number terminate?

**Theorem**: A rational number (in lowest terms) has a terminating decimal expansion if and only if has the form **2ᵐ × 5ⁿ** (m, n ≥ 0).

**Examples**:
- → terminates → terminates → does NOT terminate… recurring.)
- → does NOT terminate (because of the 3).

**Why**: any decimal expansion is a fraction with denominator 10ⁿ = 2ⁿ × 5ⁿ. To convert to decimal form, you need to ONLY have 2s and 5s as primes — otherwise you can't multiply numerator/denominator into a power of 10.

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