QQuestionMathematics
QuestionMathematics
Why are there 52 weeks in a year and not 48 weeks, given that there are only 4 weeks per month (4 x 12 = 48)?
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Answer
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Step 1:I'll solve this problem step by step, explaining the discrepancy between calendar weeks and months.
Step 2:: Understanding Month Length
Most months are actually longer than exactly 4 weeks. While 4 × 12 = 48 weeks would seem logical, the actual calculation is more nuanced.
Step 3:: Precise Month Length Calculation
A typical month ranges between 28 and 31 days: - 28 days (February in non-leap years) - 30 days (April, June, September, November) - 31 days (January, March, May, July, August, October, December)
Step 4:: Week Length Conversion
1 \text{ week} = 7 \text{ days}
Step 5:: Average Month Length
Average month length: $$\frac{(28 + 30 + 31 \times 7)}{12} \approx 30.44 \text{ days}
Step 6:: Weeks per Year Calculation
365.25 \text{ days} \div 7 \text{ days per week} \approx 52.18 \text{ weeks}
Final Answer
There are 52 weeks in a year because the average month is slightly longer than exactly 4 weeks, resulting in a total of approximately 52.18 weeks annually.
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