A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year.
How accurate is this watch, expressed as a percentage?
Express 8 seconds as a fraction of the number of seconds in a year. Then change that fraction to %
8/(24*365*3600) = 2.5*10^-7
= ____ %
0.2
100
2.5*(10^-9)%
A watch manufacturer claims that its watches gain or lose no more than 8s in a year.
To determine the accuracy of the watch as a percentage, you need to calculate the maximum possible time deviation, and then express it as a percentage of one year.
The manufacturer claims that the watch gains or loses no more than 8 seconds in a year. This means that the watch's accuracy is within a range of ±8 seconds.
To calculate the maximum possible time deviation, you add the positive and negative values together:
Max Deviation = 8 seconds (positive) + 8 seconds (negative) = 16 seconds
Next, you need to express this time deviation as a percentage of one year (which is 365 days or 31,536,000 seconds):
Accuracy = (Max Deviation / One year) × 100
Accuracy = (16 seconds / 31,536,000 seconds) × 100
Now, let's calculate the accuracy:
Accuracy = 0.000051 seconds × 100
Accuracy ≈ 0.000051%
Therefore, the accuracy of the watch is approximately 0.000051%, which can be rounded to 0.0001%.
It's important to note that this calculation assumes that the time deviation is evenly distributed throughout the year. Additionally, other factors like external conditions or the watch's aging may affect its accuracy.