15.01 Units of time
$12$12 or $24$24 hour time
We are used to using a standard $12$12 hour clock to express time, but it is also possible to use a $24$24 hour clock. Instead of thinking of a day as two blocks of $12$12 hours, we can think of it as one block of $24$24 hours. It's useful for noting the time without having to use am (before midday) or pm (midday, and after) next to the time. In the following image, observe the time on the clock. This time has been written on either side in both $12$12 and $24$24 hour format.
- Converting from the $12$12 hour clock to the $24$24 hour clock, add $12$12 to any hour after midday
- Converting from the $24$24 hour clock to the $12$12 hour clock, subtract $12$12 from any hour after $12$12 and add on the "pm". For any time less than $12$12, just add on the "am".
Have a look at the comparison chart below.
| $12$12 hour clock | $24$24 hour clock |
|---|---|
| $12:00$12:00 am (midnight) | $00:00$00:00 (midnight) |
| $1:00$1:00 am | $01:00$01:00 |
| $2:00$2:00 am | $02:00$02:00 |
| $3:00$3:00 am | $03:00$03:00 |
| $4:00$4:00 am | $04:00$04:00 |
| $5:00$5:00 am | $05:00$05:00 |
| $6:00$6:00 am | $06:00$06:00 |
| $7:00$7:00 am | $07:00$07:00 |
| $8:00$8:00 am | $08:00$08:00 |
| $9:00$9:00 am | $09:00$09:00 |
| $10:00$10:00 am | $10:00$10:00 |
| $11:00$11:00 am | $11:00$11:00 |
| $12:00$12:00 pm (midday) | $12:00$12:00 (midday) |
| $1:00$1:00 pm | $13:00$13:00 |
| $2:00$2:00 pm | $14:00$14:00 |
| $3:00$3:00 pm | $15:00$15:00 |
| $4:00$4:00 pm | $16:00$16:00 |
| $5:00$5:00 pm | $17:00$17:00 |
| $6:00$6:00 pm | $18:00$18:00 |
| $7:00$7:00 pm | $19:00$19:00 |
| $8:00$8:00 pm | $20:00$20:00 |
| $9:00$9:00 pm | $21:00$21:00 |
| $10:00$10:00 pm | $22:00$22:00 |
| $11:00$11:00 pm | $23:00$23:00 |
| $12:00$12:00 am | $24:00$24:00 or $00:00$00:00 |
We can express midnight as $24:00$24:00 or $00:00$00:00 using the $24$24 hour clock. $12:01$12:01 am would be $00:01$00:01, as it's at the start of the day. When using the $12$12 hour clock, we commonly write midnight as $12:00$12:00 am, but occasionally as $0:00$0:00 am.
Practice questions
Question 1
Convert $11$11:$26$26 pm into $24$24-hour time.
$\editable{}$$\editable{}$:$\editable{}$$\editable{}$
Question 2
Convert $2$2$0$0:$5$5$9$9 into $12$12-hour time.
$\editable{}$:$\editable{}$ pm
Units of time
Seconds, minutes, and hours all are units of time. The smallest unit of the three is seconds.
It takes $60$60 seconds to make up $1$1 minute, and it takes $60$60 minutes to make up an hour.
Knowing this relationship helps us to convert between seconds, minutes, and hours. We can use multiplication and division to change between them. If we want to know how many seconds are in $5$5 minutes of time, we can multiply that by $60$60 seconds because there are $60$60 seconds for each minute. $5\times60=300$5×60=300, so there are $300$300 seconds in $5$5 minutes.
| $1$1 Week | $=$= | $7$7 Days |
| $1$1 Day | $=$= | $24$24 Hours |
| $1$1 Hour | $=$= | $60$60 Minutes |
| $1$1 Minute | $=$= | $60$60 Seconds |
Practice questions
Question 3
How many seconds are there in $10$10 minutes?
Question 4
It takes around $300$300 minutes to drive from Sydney to Thredbo.
How many hours is this?
Question 5
Han boils an egg for $360$360 seconds.
How many minutes is this?
Question 6
If an average person sleeps for $8$8 hours a night, how many weeks does an average person spend asleep in $65$65 years? Ignore leap years.
Give your answer correct to one decimal place.
Using the calculator for time calculations
Most scientific calculators will have a button that looks like this: 
This is the "degrees, minutes, seconds" (DMS) button that we can use for angles and time calculations.
For example, if we wanted to calculate hour many hours and minutes there are in $312$312 minutes, we can put it in the calculator using the DMS button, entering $0$0 degrees and $312$312 minutes.
We read the answer to be $5$5 hours and $12$12 minutes.
CAS or graphics calculators will have this feature too but it may not be a button which looks like the one described above. Try to become familiar with the features on your calculator and use this feature to answer the question below.
Practice questions
Question 7
Convert $4545$4545 seconds into hours, minutes, and seconds.
$4545$4545 seconds is equal to $\editable{}$ hour, $\editable{}$ minutes, and $\editable{}$ seconds.