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5) Assume that ¤,t and represent progressively larger units in base-five. (a) A student expressed the amount 000 000 000 As 369five- Explain why they're incorrect and represent this number correctly both as a concrete representation and in numeration in base 5.

5) Assume that ¤,t and represent progressively larger units in base-five. (a) A student expressed the amount 000 000 000 As 369five- Explain why they're incorrect and represent this number correctly both as a concrete representation and in numeration in base 5.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Base-Five Numeration Exercise** **Problem 5:** Assume that a small square (◻), a rectangle (▭), and a larger square (⬛) represent progressively larger units in base-five. **(a)** A student expressed the amount as shown using these shapes: - Three large squares (⬛⬛⬛) - Six rectangles (▭▭▭▭▭▭) - Nine small squares (◻◻◻◻◻◻◻◻◻) This representation was labeled as 369\(_{five}\). **Task:** Explain why this representation is incorrect. Provide a corrected version of this number both as a concrete representation using the shapes and in numerical form in base-five. Consider that each type of shape represents the following units: - ◻ = 1 - ▭ = 5 - ⬛ = 25 **Discussion:** In base-five, each digit should be less than five. The student’s representation does not adhere to this rule, as they used digits (3, 6, 9) equal to or greater than five. To correct this: - Convert the given quantities to base-five correctly, ensuring each digit is less than five. - Express the corrected number using the provided shapes.
Transcribed Image Text:**Base-Five Numeration Exercise** **Problem 5:** Assume that a small square (◻), a rectangle (▭), and a larger square (⬛) represent progressively larger units in base-five. **(a)** A student expressed the amount as shown using these shapes: - Three large squares (⬛⬛⬛) - Six rectangles (▭▭▭▭▭▭) - Nine small squares (◻◻◻◻◻◻◻◻◻) This representation was labeled as 369\(_{five}\). **Task:** Explain why this representation is incorrect. Provide a corrected version of this number both as a concrete representation using the shapes and in numerical form in base-five. Consider that each type of shape represents the following units: - ◻ = 1 - ▭ = 5 - ⬛ = 25 **Discussion:** In base-five, each digit should be less than five. The student’s representation does not adhere to this rule, as they used digits (3, 6, 9) equal to or greater than five. To correct this: - Convert the given quantities to base-five correctly, ensuring each digit is less than five. - Express the corrected number using the provided shapes.
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