# Mathedu

Learn math by practice

# Re-engineering Math

## The Measurement of Time II: the time on the clock

The day is the smallest time unit that has an astronomic reference: the time by which the earth spins on itself by one turnaround.

But it is not the smallest duration we may evaluate: our clocks show us the hours and minutes, and even the seconds.

These are obtained from the day duration by successive divisions:

• The hour is the 24th part of the day, that is that 1 day lasts 24 hours of same duration.
• The minute is the 60th part of the hour: an hour lasts 60 minutes
• The second is the 60th part of the minute: a minute lasts 60 seconds, and an hour lasts 60x60=3,600 seconds.

We give the time in hours and minutes after midnight (am) or noon (pm). Indeed, the day of 24 hours is divided into 2 periods of 12 hours each, one from midnight to noon, and the other from noon to next midnight.

We also usually tell the time it is in parts of hours or minutes before or after the full hour:

• a quarter to 9 is 8:45 am in the morning and 8:45 pm in the evening.
• 10 to 8 is 7:50 am in the morning and 7:50 pm in the evening
• half past 3 is 3:30 am in the night and 3:30 pm in the afternoon
• 5 past 6 is 6:05 am in the morning and 6:05 pm in the evening

The international (and French) convention to give a time during the whole day is to give:

• the same time for an "am" time: 7:05 am is 7:05
• the time augmented by 12 hours for a "pm" time: 6:50 pm is 18:50

That's the time since last midnight, midnight being 0:00 and noon being 12:00.

And what about the seconds? It is a way to measure short times, of less than 1 minute or of just a few minutes and some… seconds.

For instance, you may measure your heart beats rythm in counting your beats on your wrist during the time your clock counts 60 seconds (numbers from 1 to 60 or a turnaround of the second hand).

You may do it more rapidly by counting the beats during 15 seconds, that are a quarter of a minute (60/4=15), and then multiply the result by 4.

The seconds are also the unit to measure a sports performance, but with decimal digits: the Men's 100 metres world record is 9.58 seconds which was run by Usain Bolt.

The seconds and hundredth of seconds are measured by the chronometers.

The calendars, the clocks and the chronometers are complementary means of measuring the time, each for a different scale…