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Without actual performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminationg repeating decimal expansion :
(i) `(12)/(125)` (ii) `(7)/(1600)` (iii) `(11)/(3125)`

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AI Generated Solution

To determine whether the given rational numbers will have a terminating or non-terminating repeating decimal expansion, we need to analyze their denominators after simplifying them into their prime factors. A rational number will have a terminating decimal expansion if its denominator (in simplest form) can be expressed as \(2^m \times 5^n\), where \(m\) and \(n\) are non-negative integers. Let's analyze each of the given rational numbers step by step: ### (i) \( \frac{12}{125} \) 1. **Factor the numerator and denominator:** - Numerator: \(12 = 2^2 \times 3\) ...
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