$1+\frac{24}{60}+\frac{51}{60^2}+\frac{10}{60^3}
Answer (1)
Calculate each term: 1 , 60 24 = 0.4 , 6 0 2 51 = 0.0141 6 , 6 0 3 10 = 0.000046296...
Add the terms together: 1 + 0.4 + 0.0141 6 + 0.000046296... = 1.41421296296...
Recognize that the result is approximately equal to 2 .
The final answer is 1.41421296296
Explanation
Understanding the Expression We are asked to evaluate the expression 1 + 60 24 + 6 0 2 51 + 6 0 3 10 . This looks like a base-60 representation of a number. Let's calculate the value.
Calculating Each Term First, we calculate each term individually:
1 = 1 60 24 = 0.4 6 0 2 51 = 3600 51 = 0.0141 6 6 0 3 10 = 216000 10 = 0.000046296...
Summing the Terms Now, we add these values together:
1 + 0.4 + 0.0141 6 + 0.000046296... = 1.41421296296...
This value is very close to 2 ≈ 1.41421356...
Final Result Therefore, the expression evaluates to approximately 1.41421296296... , which is very close to 2 .
Examples
Understanding different number systems like base-60 can help in various fields, such as computer science (binary, hexadecimal), timekeeping (seconds, minutes, hours), and even in understanding historical measurement systems. For instance, the Babylonians used a base-60 system, which is why we have 60 seconds in a minute and 60 minutes in an hour. Evaluating expressions in different bases enhances our ability to work with and convert between various numerical representations, which is crucial in many technical and scientific applications.
