A rational number in its lowest form has denominator 2³ × 5. How many decimal places will its decimal expansion have? Explain your answer.
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Question

A rational number in its lowest form has denominator 23 × 5. How many decimal places will its decimal expansion have? Explain your answer.

KnowledgeBoat · Accepted Answer

Given: Denominator (in lowest form) = 23 × 5. Since the denominator has only 2's and 5's as prime factors, the decimal expansion is terminating. The number of decimal places in the terminating decimal expansion of (in lowest form) is the maximum of m and n. Here, m = 3 (power of 2) and n = 1 (power of 5). ⇒ Number of decimal places = max(3, 1) = 3. To verify, multiply numerator and denominator by 52 to make denominator a power of 10 : Dividing by 1000 gives a decimal with 3 decimal places. Hence, the decimal expansion will have 3 decimal places.

Mathematics

A rational number in its lowest form has denominator 2³ × 5. How many decimal places will its decimal expansion have? Explain your answer.

Whole Numbers

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