Convert units of time
Theory
Converting units of time is a Year 4 measurement skill: changing between seconds, minutes, hours, days and weeks. You multiply to change a bigger unit into a smaller one and divide to go the other way, using 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day and 7 days in a week. Curriculum: VC2M4M03 / AC9M4M03.
Time is measured in different units. From shortest to longest, the everyday units are seconds, minutes, hours, days and weeks. Each unit is joined to the next by a fixed fact: \(1\) minute is \(60\) seconds, \(1\) hour is \(60\) minutes, \(1\) day is \(24\) hours, and \(1\) week is \(7\) days.
To convert a time means to write the same amount using a different unit. There are only two moves. To change a bigger unit into a smaller one, you multiply. To change a smaller unit into a bigger one, you divide.
For example, \(10\) minutes is \(10 \times 60 = 600\) seconds, and \(540\) seconds is \(540 \div 60 = 9\) minutes. Sometimes a time is written in mixed units, such as \(1\) hour \(15\) minutes, which is the same as \(60 + 15 = 75\) minutes.
These time facts do not change. Keep them handy and you can convert any time by multiplying or dividing.
| 1 of this unit | is the same as |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 day | 24 hours |
| 1 week | 7 days |
| 1 year | 12 months |
| 1 year | 365 days (366 in a leap year) |
How to convert a unit of time
- Name the units. Write down the unit you have and the unit you want, such as minutes to seconds.
- Pick the move. Going to a smaller unit means multiply; going to a bigger unit means divide.
- Use the fact. Multiply or divide by the matching number: \(60\) for minutes and seconds, \(60\) for hours and minutes, \(24\) for days and hours, or \(7\) for weeks and days.
- Check it makes sense. A smaller unit should give a bigger number, and a bigger unit should give a smaller number.
Mixed units
- Hours and minutes to minutes: multiply the hours by \(60\), then add the extra minutes. The same works for minutes and seconds.
- Minutes to hours and minutes: take out as many groups of \(60\) as you can. Each group is \(1\) hour; what is left over is the minutes.
- Adding times: add in the same unit first, then convert the total if you need to.
Seconds are smaller than minutes, so multiply by \(60\).
| \(1\text{ min}\) | \(=\) | \(60\text{ s}\) |
| \(7 \times 60\) | \(=\) | \(420\text{ s}\) |
So \(7\) minutes \(= 420\) seconds.
Minutes are bigger than seconds, so divide by \(60\).
| \(60\text{ s}\) | \(=\) | \(1\text{ min}\) |
| \(660 \div 60\) | \(=\) | \(11\text{ min}\) |
So \(660\) seconds \(= 11\) minutes.
Hours are smaller than days, so multiply by \(24\).
| \(1\text{ day}\) | \(=\) | \(24\text{ h}\) |
| \(3 \times 24\) | \(=\) | \(72\text{ h}\) |
So \(3\) days \(= 72\) hours.
Take out whole hours first. Each \(60\) minutes is \(1\) hour.
| \(170\) | \(=\) | \(120 + 50\) |
| \(120\text{ min}\) | \(=\) | \(2\text{ h}\) |
| \(170\text{ min}\) | \(=\) | \(2\text{ h } 50\text{ min}\) |
So \(170\) minutes \(= 2\) hours \(50\) minutes.
Change the hour into minutes, then add the extra minutes.
| \(1\text{ h}\) | \(=\) | \(60\text{ min}\) |
| \(60 + 35\) | \(=\) | \(95\text{ min}\) |
So \(1\) hour \(35\) minutes \(= 95\) minutes.
Add the seconds first, then divide by \(60\).
| \(270 + 210\) | \(=\) | \(480\text{ s}\) |
| \(480 \div 60\) | \(=\) | \(8\text{ min}\) |
The two songs last \(8\) minutes altogether.
Common pitfalls
Frequently asked questions
How do you change minutes into seconds?
Multiply by \(60\), because \(1\) minute is \(60\) seconds. For \(8\) minutes, \(8 \times 60 = 480\) seconds.
How do you change seconds into minutes?
Divide by \(60\), because \(60\) seconds make \(1\) minute. For \(720\) seconds, \(720 \div 60 = 12\) minutes.
How many hours are in a day?
There are \(24\) hours in one day. To change days into hours you multiply by \(24\), so \(4\) days \(= 96\) hours.
How many days are in a week?
There are \(7\) days in one week. To change weeks into days you multiply by \(7\), so \(5\) weeks \(= 35\) days.
How do you write 110 minutes in hours and minutes?
Take out one hour first. \(110 = 60 + 50\), and \(60\) minutes is \(1\) hour, so \(110\) minutes is \(1\) hour \(50\) minutes.
How do you compare two times with different units?
Change both times into the same unit, usually seconds, then compare the numbers. For example, \(6\) minutes is \(360\) seconds, which is more than \(350\) seconds.