Answer:
- estimate: $35.00 per hour
- actual: $34.42 per hour
- within 2%, quite reasonable
Explanation:
You want to use rounding and approximation to compute the hourly wage of a person working 40 hours per week and making $71,600 per year. You also want a reasonableness check compared to the actual answer.
Estimate
Rounding the $71,600 salary to the nearest $10,000, it becomes $70,000. Considering 50 weeks per year and 40 hours per week, the number of hours in a year is approximated by 40×50 = 2000. Then the hourly wage is approximately ...
$70,000/(2000 h) = $35/h . . . . estimated wage
Check
If we assume exactly 52 weeks in a year, there are 40×52 = 2080 working hours in a year. That means the hourly wage is actually ...
$71,600/(2080 h) ≈ $34.42 . . . . actual hourly wage
The difference of the estimate from the actual value is ...
$34.42 -35.00 = -$0.58
That is the actual value is between 1% and 2% lower than the estimate, a quite reasonable error. (Often anything within 10% is a reasonable estimate.)
__
Additional comment
Often, when doing estimates, you want to estimate the error in your estimating process. Here, there are two contributors.
Rounding 71,600 down to 70,000 reduces the value by a factor of 700/716, or 175/179. That means the error will be about 4 parts in 180 (an estimate), or 1 part in 45, about 2.2% (low).
Rounding 52 weeks per year down to 50 increases the value by a factor of 52/50 = 1.04, causing the estimated value to be about 4% high. These two errors are in opposite directions, so the net effect is an estimated error of about 4% -2.2% = 1.8% (high).
The error estimate has errors of its own, but this gets you in the ballpark of approximate error in the estimated value.
A year of 365 days is 52 weeks plus one day, so can be 2088 working hours. Using this value for hours reduces the hourly wage to about $34.29.