Units of Time (HSC SSCE Mathematics Standard): Revision Notes
Units of Time
What is time?
Time describes the continuous flow of events happening in the past, present, and future. We measure time using several different units including seconds, minutes, hours, days, weeks, months, and years.
One complete year represents the time it takes for Earth to travel around the Sun, which is approximately days. This extra quarter day is why we have leap years every four years!
To help remember how many days are in each month:
- September, April, June, and November each have days
- All other months have days, except February
- February has days in regular years and days in leap years
We use clocks and other timing devices to measure and display time.
Time units
Understanding the basic units of time and how they relate to each other is essential for solving time-related problems.
Standard units of time
The second is the base unit of time. All other time units are based on this fundamental unit. Here are the key relationships:
| Quantity | Name of unit | Symbol | Value |
|---|---|---|---|
| Time | Second | s | Base unit |
| Time | Minute | min | |
| Time | Hour | h | |
| Time | Day | d |
Key Relationships to Remember:
Each unit of time builds on the previous one:
- minute seconds
- hour minutes
- day hours
These conversion factors are the foundation for all time calculations!
Converting between units
When converting between different time units, you need to multiply or divide by specific conversion factors. The key principle to remember is:
- Multiply when converting to a smaller unit (e.g., hours to minutes)
- Divide when converting to a larger unit (e.g., minutes to hours)
Conversion factors
Here are the relationships you need to know:
Converting between days and hours:
- To convert days to hours: multiply by
- To convert hours to days: divide by
Converting between hours and minutes:
- To convert hours to minutes: multiply by
- To convert minutes to hours: divide by
Converting between minutes and seconds:
- To convert minutes to seconds: multiply by
- To convert seconds to minutes: divide by
Memory Aid: Think of the conversion chain:
days hours minutes seconds
Moving right (to smaller units): multiply by , then , then
Moving left (to larger units): divide by , then , then
Worked Example: Converting Units of Time
Let's work through some conversions to see how this works in practice.
Part a: Convert hours and minutes to minutes
To solve this problem, we need to convert the hours to minutes first, then add the remaining minutes.
Convert hours to minutes by multiplying by :
Add the additional minutes:
Therefore, hours and minutes equals 195 minutes.
Part b: Convert minutes to days
First, convert minutes to hours by dividing by :
Next, convert hours to days by dividing by :
Therefore, minutes equals 7 days.
Exam Tip: Most scientific calculators have a degrees-minutes-seconds (DMS) key that can help you convert between hours, minutes, and seconds quickly.
24-hour time
The 24-hour clock is a way of expressing time that runs from midnight to midnight, using numbers from to . This system is also called military time in some countries.
Understanding 24-hour notation
In 24-hour notation, time is written in the format hh
where:- hh represents hours ( to )
- mm represents minutes ( to )
The day begins at midnight, which is written as . The last minute of the day begins at .
Advantages of 24-hour time
Why Use 24-Hour Time?
The 24-hour clock is useful because it removes any confusion between morning and afternoon times. You don't need to use a.m. (ante meridiem, meaning before midday) or p.m. (post meridiem, meaning after midday) designations.
You'll find 24-hour time used in:
- Transport timetables (trains, buses, flights)
- Digital clocks and oven timers
- Airport arrival and departure boards
- Military and emergency services
Converting between 12-hour and 24-hour time
Here's how the two systems compare:
| 12-hour clock | 24-hour clock | 12-hour clock | 24-hour clock |
|---|---|---|---|
| 12:00 (midnight) | 00:00 | 12:00 (noon) | 12:00 |
| 1:00 a.m. | 01:00 | 1:00 p.m. | 13:00 |
| 2:00 a.m. | 02:00 | 2:00 p.m. | 14:00 |
| 3:00 a.m. | 03:00 | 3:00 p.m. | 15:00 |
| 4:00 a.m. | 04:00 | 4:00 p.m. | 16:00 |
| 5:00 a.m. | 05:00 | 5:00 p.m. | 17:00 |
| 6:00 a.m. | 06:00 | 6:00 p.m. | 18:00 |
| 7:00 a.m. | 07:00 | 7:00 p.m. | 19:00 |
| 8:00 a.m. | 08:00 | 8:00 p.m. | 20:00 |
| 9:00 a.m. | 09:00 | 9:00 p.m. | 21:00 |
| 10:00 a.m. | 10:00 | 10:00 p.m. | 22:00 |
| 11:00 a.m. | 11:00 | 11:00 p.m. | 23:00 |
Conversion Rules:
- For morning times (a.m.): The 24-hour time is the same as the 12-hour time
- For afternoon/evening times (p.m.): Add to the hour (except for 12:00 p.m. which stays as 12:00)
- To convert back from 24-hour to 12-hour: If the hour is greater than , subtract and add p.m.
Worked Example: Using 24-Hour Time
Let's practice converting between the two formats and calculating time differences.
Part a: Convert 8:15 p.m. to 24-hour time
Since 8:15 p.m. is an afternoon time, we add to the hour:
The minutes stay the same.
Therefore, 8:15 p.m. in 24-hour time is 20:15.
Part b: Write 21:45 in 12-hour time
Since the hour () is greater than , this is an afternoon time.
Subtract from the hour:
The minutes stay the same. Add p.m. to show it's in the afternoon.
Therefore, 21:45 in 12-hour time is 9:45 p.m.
Part c: How long is it between 18:00 and 23:15?
To find the time difference, subtract the earlier time from the later time:
This means there are 5 hours and 15 minutes between 18:00 and 23:15.
Exam Tip: When subtracting times, line up the hours and minutes separately. If you need to borrow from the hours to the minutes, remember that hour equals minutes.
Key Points to Remember:
-
The base unit of time is the second (s). Other units build on this: minute seconds, hour minutes, and day hours.
-
When converting units, multiply to convert to smaller units and divide to convert to larger units (e.g., multiply by to convert hours to minutes, divide by to convert minutes to hours).
-
24-hour time uses the format hh
and runs from 00:00 (midnight) to 23:59, eliminating the need for a.m. and p.m. designations. -
To convert 12-hour p.m. times to 24-hour format, add 12 to the hour (except for 12:00 p.m.). To convert back, subtract 12 from hours greater than 12.
-
Always show your working when converting between time units or calculating time differences - this helps you track your steps and avoid errors.