Question 14 - Figure it out - Page 44, 45 - Chapter 2 Class 8 - Power Play (Ganita Prakash)

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Question 14 What was the date 1 arab/1 billion seconds ago?1 arab or 1 billion = 109 Thus, we need to find the date 109 seconds ago Let’s convert 109 seconds into years and days Converting 1 day into seconds Since 1 day has 24 hours, 24 hours = 1 day 1 hour = 1/24 day 60 minutes = 1/24 day 1 minute = 1/24 ×1/60 day 60 seconds = 1/24 ×1/60 day 1 second = 𝟏/𝟐𝟒 ×𝟏/𝟔𝟎 ×𝟏/𝟔𝟎 day Thus, we can say 109 seconds = 10^9 × 1/24 ×1/60 ×1/60 days = 10^9 × 1/(24 × 6 × 6) ×1/100 days = 10^9 × 1/(24 × 36) ×1/100 days = 〖𝟏𝟎〗^𝟗 × 1/864 ×1/100 days = 〖𝟏𝟎〗^(𝟓 + 𝟒) × 1/864 ×1/100 days Applying am × an = am+n = 〖𝟏𝟎〗^𝟓 × 〖𝟏𝟎〗^𝟒 × 1/864 ×1/100 days We know that 365 days = 1 year 1 day = 𝟏/𝟑𝟔𝟓 year Thus, 11,574 days = 11574/365 year = 31.7 years Finding Date now Current Date: August 11, 2025. Calculation: Go back 31 years: August 11, 1994. Go back the remaining 0.7 years: 0.7×365.25≈256 days. We need to find the date that is 256 days before August 11, 1994. Counting back the days through the months: Aug: 11 days Jul: 31 days Jun: 30 days May: 31 days Apr: 30 days Mar: 31 days Feb: 28 days Jan: 31 days This totals 223 days, taking us to January 1, 1994. We still need to go back 256−223=33 more days into 1993. Going back 31 days from December 31, 1993 lands on December 1. We need to go back 2 more days. Answer: The date was approximately November 29, 1993. = 〖𝟏𝟎〗^𝟓 × 〖𝟏𝟎〗^𝟒 × 1/864 ×1/100 days = 1,00,000 × 1/864 ×1/100× 10^4days = 1,00,000/100 × 1/864 × 10^4days = 1000 × 1/864 × 10^4days = 1000/864 × 10^4days = 1.1574 × 〖𝟏𝟎〗^𝟒days (approx.) = 11,574 days (approx.) Thus, 109 seconds = 11,574 days approximately Now, we convert 11,574 days into years