Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: , and . Then check your answers by explicitly performing the long divisions and expressing these rational numbers as decimals.

Question

KnowledgeBoat · Accepted Answer

To determine if a rational number in lowest form has a terminating decimal expansion, the prime factorisation of q must contain only 2's and/or 5's. (i) Prime factorisation of 20 = 22 × 5. Since the denominator has only 2's and 5's, it is a terminating decimal. Performing long division : ⇒ = 0.35 (ii) Prime factorisation of 15 = 3 × 5. Since the denominator has 3 (a prime other than 2 or 5), it is a repeating decimal. Performing long division : ⇒ (iii) Prime factorisation of 250 = 2 × 53. Since the denominator has only 2's and 5's, it is a terminating decimal. Performing long division : ⇒ = 0.052 Hence, (terminating), (repeating) and (terminating).

Mathematics

Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: , and . Then check your answers by explicitly performing the long divisions and expressing these rational numbers as decimals.

Whole Numbers

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