CBSE Class 8 Number System Important Case Studies
CBSE Class 8 Number System Important Case Studies help students strengthen their understanding of rational numbers, integers, and decimals. These case studies are designed to enhance logical reasoning, analytical skills, and conceptual clarity in mathematics. Moreover, they provide practical examples for better comprehension.
Why Practice Number System Case Study Questions?
Practicing CBSE Class 8 Number System Case Study Questions allows learners to master topics such as laws of exponents and decimal representation. Additionally, these case studies improve accuracy and confidence during exams. Therefore, solving them regularly is highly recommended for better scores and deeper understanding.
Learn Through Video Tutorials
Students can explore CBSE Class 8 Number System video tutorials that explain every concept step-by-step. Consequently, video lessons make learning more interactive and engaging. In addition, they support visual understanding of difficult mathematical problems efficiently.
Case Study 2: Case study number system for class 8 math
A naval research vessel is testing a new submarine depth monitoring system in the Indian Ocean. The submarine performs a series of dives and ascents over a 6-hour period, with depth readings taken every hour. The depth changes (in meters) from sea level are recorded as: +150, -320, +85, -410, +120, -280, where positive values represent ascent and negative values represent descent. The monitoring system uses rational numbers to calculate pressure changes, with every 10 meters of depth equivalent to 1 atmosphere of pressure. The engineers need to analyze this data to understand the submarine’s buoyancy control system and ensure it operates within safe mathematical parameters of integer and rational number operations while maintaining closure properties under various depth calculations.
Solution: Net change = 150 + (-320) + 85 + (-410) + 120 + (-280) = (150+85+120) + (-320-410-280) = 355 + (-1010) = -655 meters.
Solution: Cumulative depths: Hour 1: 150, Hour 2: 150-320=-170, Hour 3: -170+85=-85, Hour 4: -85-410=-495, Hour 5: -495+120=-375, Hour 6: -375-280=-655. Maximum depth = 495 meters (absolute value of -495). Note: There appears to be an error in the options as 495m is not listed. The closest option is 555m.
Solution: Maximum depth = 495 meters = 49.5 atmospheres, Minimum depth = 150 meters = 15 atmospheres. Ratio = 49.5/15 = 495/150 = 33/10 in simplest form, but as given 49.5/15.
Solution: When we multiply depth in meters by 1/10 to get atmospheres, we get another rational number, demonstrating closure property under multiplication.
Solution: Distances: H1-H2: |150-(-320)|=470, H2-H3: |-320-85|=405, H3-H4: |85-(-410)|=495, H4-H5: |-410-120|=530, H5-H6: |120-(-280)|=400. Greatest distance is 530 meters from Hour 4 to Hour 5.