Number System Practice Case Study Class 8 PDF Download
The Number System Practice Case Study Class 8 PDF Download helps students revise important concepts like whole numbers, integers, and rational numbers. Moreover, it provides solved examples and exercises designed according to CBSE and DAV guidelines. Students can strengthen their mathematical foundation through daily practice.
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Case Study 5: Math Case Study Class 8 for CBSE and ICSE students
An oceanographic research team is studying thermal layers in the Pacific Ocean at a specific location. They measure temperatures at different depths: Surface (0m): 28.0°C, 100m: 15.5°C, 200m: 8.25°C, 300m: 4.125°C, 400m: 2.0625°C. The researchers notice a fascinating mathematical pattern in the temperature decay with depth. Each temperature measurement can be expressed as a rational number, and the sequence follows a precise mathematical relationship. The team needs to analyze this pattern using number system concepts, particularly focusing on the properties of rational numbers, their operations, and representations. This analysis is crucial for developing predictive models of ocean thermal behavior and understanding how rational number operations apply to real-world scientific data collection and interpretation in marine environments.
Solution: Checking ratios: 15.5/28.0 = 31/56 ≈ 0.553, 8.25/15.5 = 33/62 = 0.532, 4.125/8.25 = 0.5, 2.0625/4.125 = 0.5. The pattern stabilizes at exactly 1/2 from 200m downward.
Solution: The pattern from 200m: 8.25 = 33/4, 300m: 4.125 = 33/8, 400m: 2.0625 = 33/16, so 500m: 33/32 = 1.03125°C.
Solution: The product of any two rational numbers is always a rational number, demonstrating the closure property under multiplication.
Solution: Temperatures: 28.0 = 28/1, 15.5 = 31/2, 8.25 = 33/4, 4.125 = 33/8, 2.0625 = 33/16. Sum = 28/1 + 31/2 + 33/4 + 33/8 + 33/16 = 448/16 + 248/16 + 132/16 + 66/16 + 33/16 = 927/16. Average = 927/16 ÷ 5 = 927/80.
Solution: For symmetry about 10°C: 10 – x = y – 10 or x + y = 20. Checking pairs: 100m (15.5) and 300m (4.125): 15.5 + 4.125 = 19.625 (close to 20). 200m (8.25) and itself: 8.25 + 8.25 = 16.5. The pair 100m and 300m is most symmetric about 10°C.