1. **Problem Statement:** Find the approximate and exact number of days between the given date ranges. 2. **Important Notes:** - Year 2000 is a leap year (366 days). - Year 2001 is not a leap year (365 days). - For approximate calculations, assume 30 days per month. --- ### a. February 20 to October 16, 2000 (Leap Year) 3. **Exact calculation:** - Days remaining in February after 20th: $29 - 20 = 9$ days (Feb has 29 days in leap year) - March: 31 days - April: 30 days - May: 31 days - June: 30 days - July: 31 days - August: 31 days - September: 30 days - October up to 16th: 16 days 4. Sum all days: $$9 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 16 = 239$$ days 5. **Approximate calculation:** - Number of months between Feb 20 and Oct 16 is about 8 months - Approximate days: $8 \times 30 = 240$ days --- ### b. March 2, 2000 to September 18, 2001 6. **Exact calculation:** - From March 2, 2000 to March 2, 2001: 366 days (leap year) - From March 2, 2001 to September 18, 2001: - March 2 to March 31: $31 - 2 = 29$ days - April: 30 days - May: 31 days - June: 30 days - July: 31 days - August: 31 days - September 1 to 18: 18 days 7. Sum days from March 2 to September 18, 2001: $$29 + 30 + 31 + 30 + 31 + 31 + 18 = 200$$ days 8. Total days: $$366 + 200 = 566$$ days 9. **Approximate calculation:** - From March 2, 2000 to September 18, 2001 is about 18.5 months - Approximate days: $18.5 \times 30 = 555$ days --- ### c. January 12 to December 17, 2001 (Non-leap year) 10. **Exact calculation:** - Days remaining in January after 12th: $31 - 12 = 19$ days - February: 28 days - March: 31 days - April: 30 days - May: 31 days - June: 30 days - July: 31 days - August: 31 days - September: 30 days - October: 31 days - November: 30 days - December up to 17th: 17 days 11. Sum all days: $$19 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 17 = 339$$ days 12. **Approximate calculation:** - Number of months between Jan 12 and Dec 17 is about 11 months - Approximate days: $11 \times 30 = 330$ days --- ### d. October 16, 2020 to Christmas Day (December 25), 2021 13. **Exact calculation:** - From October 16, 2020 to October 16, 2021: 365 days (2021 not leap year) - From October 16, 2021 to December 25, 2021: - October 16 to October 31: $31 - 16 = 15$ days - November: 30 days - December 1 to 25: 25 days 14. Sum days from October 16 to December 25, 2021: $$15 + 30 + 25 = 70$$ days 15. Total days: $$365 + 70 = 435$$ days 16. **Approximate calculation:** - From October 16, 2020 to December 25, 2021 is about 14 months - Approximate days: $14 \times 30 = 420$ days --- **Final answers:** - a) Exact: 239 days, Approximate: 240 days - b) Exact: 566 days, Approximate: 555 days - c) Exact: 339 days, Approximate: 330 days - d) Exact: 435 days, Approximate: 420 days