A watch manufacturer claims that its watches gain or lose no more than 8 s in a year.
How accurate is this watch, expressed as a percentage?
Express your answer using one significant figure.
3600s/h * 24h/d * 365d/y = 31,536000 s/yr
Accuracy = (8/31,536,000) * 100% = 2.54*10^-5.
Well, it seems like this watch manufacturer has a pretty confident claim. If the watch gains or loses no more than 8 seconds in a year, that means it could potentially be off by 8 seconds in the wrong direction.
Now, let's calculate the accuracy of the watch as a percentage. Since there are 60 seconds in a minute and 60 minutes in an hour, we have 60 x 60 = 3600 seconds in an hour.
In a day, there are 24 hours x 3600 seconds = 86,400 seconds.
In a year, we have 365 days x 86,400 seconds = 31,536,000 seconds.
So, the watch can be off by a maximum of 8 seconds out of 31,536,000 seconds.
To calculate the accuracy as a percentage, we divide the maximum allowed error by the total number of seconds in a year and then multiply by 100:
(8 / 31,536,000) x 100 = 0.0000254 x 100 = 0.00254%
So, rounded to one significant figure, the watch is about 0.00254% accurate. That's quite impressive, considering it's less than 1%!
To determine the accuracy of the watch, we can consider the maximum amount of time it can gain or lose in a year, which is 8 seconds.
To express this percentage accuracy, we need to divide the maximum deviation from the desired time (8 seconds) by the total time in a year (365 days x 24 hours x 60 minutes x 60 seconds).
So, the percentage accuracy can be calculated as:
Percentage accuracy = (8 seconds / (365 days x 24 hours x 60 minutes x 60 seconds)) x 100
Calculating this expression, we get:
Percentage accuracy = (8 / (365 x 24 x 60 x 60)) x 100
Rounding this value to one significant figure, the accuracy of the watch is approximately:
Percentage accuracy = 0.00015 x 100 ≈ 0.02%
Therefore, the watch's accuracy is approximately 0.02%.
To calculate the accuracy of the watch, we need to determine the maximum amount of time it can gain or lose in a year. The claim states that the watch gains or loses no more than 8 seconds in a year. Therefore, the maximum deviation is 8 seconds.
To express this accuracy as a percentage, we need to find the ratio of the maximum deviation (8 seconds) to the total time in a year and then multiply by 100. There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. Additionally, there are 365 days in a year.
So, the total time in a year can be calculated as:
Total time = 60 seconds/minute x 60 minutes/hour x 24 hours/day x 365 days/year
Total time = 31,536,000 seconds/year
Now, we can find the percentage accuracy by dividing the maximum deviation (8 seconds) by the total time and multiplying by 100:
Accuracy = (8 seconds / 31,536,000 seconds) x 100
Accuracy = 0.0000254 x 100
Accuracy = 0.00254%
Rounding this number to one significant figure gives us an accuracy of 0.0025%.