Formulas
Given below are the different units of time. To convert a unit of time from a smaller unit like seconds to a larger unit like hours, the smaller unit needs to be divided with the respective numbers as given in the list below. On the other hand, to convert a larger unit of time to a smaller unit, multiply the given unit with the required number.
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- 1 day = 24 hours
- 1 week = 7 days
- 1 month = 30 or 31 days
- 1 year = 12 months
- 1 year = 52 weeks
- 1 year = 365 days (366 days for leap year)
Rapid Recall
This is how we can visualize the conversion of time from one unit to another.
Solved Examples - Units of time conversion formula
Question 1:
For a math test Jessica was asked to write the number of seconds there are in a day. What would her answer be?
We have seen the following conversions:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
The number of seconds in a day =\(~1~\times~24\times~60\times~60~=~86400\) seconds
Question 2:
Find the equivalent amount of time after converting the following.
1) 5 years = ___ weeks
Answer:
5 years = ____ weeks
We know that, 1 year = 52 weeks
Hence, 5 years \(=~5~\times~52~=~260\) weeks
2) 3 leap years = ___ days
Answer:
3 leap years = ___ days
We know that, 1 leap year = 366 days
Hence, 3 leap years \(=~3~\times~366~=~1098\) days
Question 3:
Celine was writing a table converting seconds to hours and hours to minutes and minutes to days. For each column, place the corresponding label from Seconds/Hours/Minutes/Days.
? | ? | ? | ? |
|---|---|---|---|
1 | 24 | 1440 | 86400 |
2 | 48 | 2880 | 172800 |
3 | 72 | 4320 | 259200 |
4 | 96 | 5760 | 345600 |
Answer:
We need to figure what each column corresponds to. To do that, let’s analyze the first row.
From the 1st row, 1 ___ = 24 ___ = 1440 ___ = 86400 ___
We are already aware of the following conversions:
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
In the conversions above, 24 hours is equal to one day. If we were to convert one day into the number of minutes, we get the following:
24 hours = 24 \(\times\) 60 = 1440 minutes
And if we were to convert 1440 minutes to seconds, we get the following result.
1440 \(\times\) 60 = 86400 seconds
So we can complete the first row as:
1 day = 24 hours = 1440 minutes = 86400 seconds
According to the results we just obtained, the labeling of the columns is as follows:
? | ? | ? | ? |
|---|---|---|---|
1 | 24 | 1440 | 86400 |
2 | 48 | 2880 | 172800 |
3 | 72 | 4320 | 259200 |
4 | 96 | 5760 | 345600 |
Question 4:
Steve ran a marathon for 246 minutes and 20 seconds. His friend Carl clocked an impressive 4:29:43 on his stopwatch. Who completed the marathon quicker ?
Solution:
To find out who completed the marathon quicker, let’s convert the time taken by Carl to complete the marathon on his stopwatch to minutes.
In Carl’s reading “4:29:43”, 4 represents the hours, 29 represents the minutes, and 43 represents the seconds. The next step is to convert the number of hours to minutes, add 29 to it and compare the time.
The standard conversion is: 1 hour = 60 minutes
Converting 4 hours to minutes we get the following,
4 \(\times\) 60 = 240 minutes
Total time taken by Carl = 240 + 29 = 269 minutes
So, Carl takes 269 minutes and 43 seconds to complete the race while Steve took 246 minutes and 20 seconds
269 minutes and 43 seconds is certainly greater than 246 minutes and 20 seconds.
Therefore, Steve finished the race faster than Carl.
Question 5:
Barry’s Chocolatiers closes the shop in \(1~\frac{3}{4}\) hours. Leonard wants to get a teddy bear, a dress, some flowers and a big box of chocolates. It will take him 25 minutes to get to Barry’s which is quite far away from where he stays. It will take him 25 minutes each to stop at the flower shop, boutique and the toy shop. Will Leonard make it to Barry’s Chocolatiers before it closes?
Solution:
We need to find the total time it would take to reach Barry’s chocolatiers after adding in the travel time as well as the time taken to cover all these stops.
Total time covered by Leonard = 25+25+25+25=100 minutes
Time left for Barry’s shop to close in minutes
\(=~1~\frac{3}{4}\times~60\)
\(=~\frac{4+3}{4}\times~60\)
\(=~\frac{7}{4}\times~60=~105\) minutes
Therefore, Leonard can reach Barry’s Chocolatier’s with five minutes to spare.
Question 6:
Gary spends 4 hours studying everyday. He spends 120 minutes less playing on the soccer field than he does studying on a day. How many minutes does Gary spend on the soccer field?
Solution:
Time spent by Gary to study = 4 hours
As per the standard method of conversion: 1 hour = 60 minutes
Time that Gary spent studying in minutes = 4 \(\times\) 60 = 240 minutes
Time spent by Gary playing in the field = 240 – 120 = 120 minutes
Therefore, Gary spends 120 minutes playing on the soccer field.
Events that occur in our daily lives, may be random or periodic. The best way to understand the occurrences of these events depends on the passage of time.
Students need to memorize different units of time conversion because we gauge the different events that happen according to the time it takes for every event. It may take a few seconds to throw a ball from one point to another. It may take one hour to travel from one place to another. If the time taken to throw the ball was expressed in hours or if the time taken to travel from one point to another was expressed in seconds, there will be situations when the numbers are very large. Verbally expressing these figures or writing them down would be difficult. This is one of the reasons why conversion helps.
In a leap year, the month of February gets an extra day, hence the total number of days sums up to 366 days instead of the regular number of 365 days.
A minute passes away very quickly. To keep track of the passing time after 60 minutes would be very difficult. This is because one would not know the number of hours that passed by without having the hour hand on the watch as well. Similarly, if the watch only has the hour hand, it would be difficult to figure out the number of minutes that would have elapsed within the span of an hour. This is because the hour hand in a watch moves very slowly. Therefore, we need both the minute hand as well as the hour-hand on the watch to know the number of minutes and the number of hours passed by.
becomes the numerator of the required fraction and the denominator is the same as that of the improper fraction. Thus, the required fraction is obtained.
There are many units smaller than a second. They are as follows:
1 millisecond \(=\frac{1}{1000}\) of a second
1 microsecond \(=\frac{1}{1000000}\) of a second
There are also units larger than a year, they are as follows:
1 decade = 10 years
1 century = 100 years
1 millennium = 1000 years