Arithmetic/Geometry » Units of time

These are the units of time you use most often in mathematics:

1 year365 days
1 day=24 hours
1 hours=60 minutes
1 minute =60 seconds
1 year12 months
1 week=7 days

Less often the following conversions are used (because of rounding off):

1 year52 weeks
1 quarter =91 days
1 month=30 days

Leap year

For convenience, we never calculate using leap years in mathematics. So that includes DWO-exercises.
You also don't know how many leap years you actually might have had, as the year 2000 was not a leap year and the year 2400 will not be either. Furthermore every year there are small corrections that are calles leap seconds.
If you want to work more precise, you can use 1 year = 365.25 days.
Are you a real precisian? See: Wikipedia - Leap year.


Example 1

You are 15 years old. How many seconds is that?

Answer:
15 × 365 × 24 × 60 × 60 = 473 040 000 seconds.

Example 2

A reservoir holds 900 km3 water.
When all the pipes of the hydro dam are opened, 2 hm3 per second will flow from the reservoir. How many days will it take for the reservoir to be emptied?

Answer:
2 hm3 = 0,002 km3.
It will take 900 : 0.002 = 450 000 seconds.
That is 450 000 : 60 : 60 : 24 = 5524 ≈ 5.2 days.

Example 3

Convert 3.62 hours to hours, minutes and seconds.

Answer:
You have 3 whole hours and another 0.62 hours, which is 0.62 × 60 = 37.2 minutes.
That is 37 minutes and another 0.2 minutes, which is 0.2 × 60 = 12 seconds.
Therefore 3.62 hours are 3 hours, 37 minutes and 12 seconds.

Example 4

Convert 0.34 hours to minutes and seconds.

Answer:
The 0.34 hours are 0.34 × 60 = 20.4 minutes. So you have 20 whole minutes.
You also have another 0.4 minutes, which is 0.4 × 60 = 24 seconds.
Therefore 0.34 hours are 20 minutes and 24 seconds.