Time & Conversion

Length and mass went decimal — converting is just multiplying by 10. Time refuses: 1 minute is 60 seconds, 1 hour is 60 minutes, 1 day is 24 hours. The units you touch most often are the least "well-behaved".

The family tree of time units

1 min = 60 s
1 h = 60 min
1 day = 24 h
1 week = 7 days
1 year ≈ 365 days

Upward, months run long and short and years run common and leap; downward, seconds split into milliseconds. Converting means knowing each level's exchange rate: hours to minutes, multiply by 60; minutes to seconds, multiply by 60; days to hours, multiply by 24.

Why 60 of all numbers

The Babylonians set this scheme thousands of years ago. Sixty is a wonderfully cooperative number: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30 all divide it — split an hour into 2, 3, 4 or 6 equal parts and every part lands on a whole number of minutes, no crumbs. Base ten only feeds 2 and 5; base sixty is far more generous. The habit survives today: a clock face is that ancient decision made visible.

Converting: multiply or divide by 60

Example: hours ↔ minutes

$2.5$ hours = $2.5 \times 60 = 150$ minutes. Backwards, $90$ minutes = $90 \div 60 = 1.5$ hours, i.e. 1 h 30 min. Going to a smaller unit, multiply by the rate; going bigger, divide — the same move as in metric units, just with 60 and 24 in place of 10.

The 12-hour and 24-hour clocks

2 pm and 14:00 are the same moment. The 12-hour clock leans on am/pm; the 24-hour clock just adds 12 to afternoon hours:

2:00 pm → $2 + 12 = 14:00$ ;
11:30 pm → 23:30;
In 24-hour time, 0:00 is midnight and 12:00 is noon.

Train tickets and airport boards prefer 24-hour time: one less am/pm mix-up is one less missed departure.

Adding up durations

The feature runs 1 h 47 min and the trailers add 12 min — how long are you in your seat, door to credits?

Example: adding durations

Add the minutes first: $47 + 12 = 59$ — short of 60, so no carry; then the hours: $1 + 0 = 1$ . Total: 1 h 59 min. When minutes overflow, carry: $45$ min $+ 30$ min $= 75$ min $= 1$ h 15 min.

Leap years in one sentence

Earth takes about 365.25 days to orbit the Sun, so roughly every 4 years February gains a day (February 29) and the year runs 366 days — a leap year.

Check yourself

Quick quiz

1. 3 hours is how many minutes?
2. In 24-hour time, 4:30 pm is written…
3. A 1 h 50 min movie plus 20 min of trailers lasts…