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In this article, we will discuss what are different units of time and how to convert one unit to another.

## What is Time?

In physics, we define time as what the clock tells us. Time is a scalar quantity and is denoted by the symbol t. We must understand the time and its units because it is helpful to derive other concepts in physics and mathematics like distance, kinetic energy, and motion.

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## SI Unit of Time

The SI (System International) unit of time is "seconds" that is denoted by the letter s.

### Other Units of Time

The other units of time are:

• Minute (min): In one minute, there are sixty seconds
• Hour (h): In one hour, there are sixty minutes
• Day: In a day, there are 24 hours
• Week: In a week there are 7 days
• Fortnight: There are 15 days in a fortnight
• Quarter: In a quarter, there are three months
• Semester: In one semester, there are six months
• Year: In a year, there are 365 days. In a leap year, there are 366 days
• Century: In a century, there are 100 years
• Millennium: In one millennium, there are 1000 years

In the next section, we will solve some examples in which we will convert one unit to another.

## Example 1

How many seconds are there in a day?

### Solution

We will convert multiple units one by one to determine the number of seconds in a day. Remember that in this example, we are converting a bigger unit to a smaller one, hence we will use the multiplication operation throughout.

Number of hours in a day = 24

Number of minutes in an hour = 60 minutes

Number of minutes in a day = 24 x 60

= 1440 minutes

Number of seconds in a minute = 60 seconds

Number of seconds in a day = 1440 x 60

= 86400 seconds

Hence, in a day there are 85400 seconds.

## Example 2

How many hours are there in three weeks?

### Solution

We will convert multiple units one by one to determine the number of hours in three weeks. Remember that in this example, we are converting a bigger unit to a smaller one, hence we will use the multiplication operation throughout.

Number of days in a week = 7 days

Number of days in three weeks = 7 x 3 = 21 days

Number of hours in a day = 24 hours

Number of hours in 21 days = 21 x 24

= 504 hours

Hence, in three weeks there are 504 hours.

## Example 2

How many minutes are there in a fortnight?

### Solution

In this example, we will again use the multiple units of time to convert fortnight into minutes. Remember that in this example, we are converting a bigger unit to a smaller one, hence we will use the multiplication operation throughout.

Number of days in a fortnight = 15 days

Number of hours in a day = 24 hours

Number of hours in a fortnight = 15 x 24  = 360 hours

Number of minutes in an hour = 60 minutes

Number of minutes in a fortnight = 360 x 60

= 21,600 minutes

Hence, in a fortnight, there are 21, 600 minutes

## Example 4

Sarah took 2 hours 46 minutes to complete her test. Her friend Mariah took 49 minutes more than Sarah to complete the same test.

a) In how many minutes, did Sarah and Mariah complete their tests?

b) How much more time (in seconds) did Mariah take to complete her test?

### Solution

There are two parts in this example, so we will complete each part one by one.

### Part a

In this example, we are given the time taken by Sarah to complete the test. First, we will convert this time in minutes to determine the time (in minutes) taken by Sarah to complete the test.

Number of minutes in a hour = 60 minutes

Number of minutes in 2 hours = 2 x 60 = 120 minutes

Time (in minutes) taken by Sarah to complete her test = 120 + 46 = 166 minutes

Time taken by Mariah to complete her test = 2 hours 46 minutes + 49 minutes

Time taken by Mariah to complete her test in minutes = 120 + 46 + 49 = 215 minutes

Now, we will proceed to the part b of the example

### Part b

Number of additional minutes taken by Mariah to complete the same test = 49 minutes

Number of seconds in a minute = 60 seconds

Number of seconds in 49 minutes = 49 x 60 seconds

= 2940 seconds

Hence, Mariah took 2940 additional seconds than Sarah to complete the same test.

## Example 5

John who was doing a full-time business decided to pursue his higher studies in business management. He got enrolled in a university in a four-year degree program. Because he was busy in his business too, so he started taking fewer courses than usual. Therefore, he took more time to complete his degree. He took half a decade, 3 months (March to May), and 7 days to complete his degree.

a) In how many days, did he complete his degree assuming that one year was a leap year?

b) How much more time (in days) did he take to complete a degree program than a student who completed his/her degree in time assuming the fact there was one leap year during this period?

### Solution

This example has two parts. We will solve each part one by one.

### Part a

First, we will determine the number of days in which John completed his degree. It is given that he took half a decade, 8 months, and 7 days to complete his degree.

Number of years in a decade = 5 years

Number of days in a year = 365 days

Number of days in a leap year = 366 days

Number of days in March = 31 days

Number of days in April = 30 days

Number of days in May = 31 days

Total number of days in half decade, 3 months and 7 days = 365 x 4 + 366 + 31 + 30 + 31

= 1925 days

Hence, John completed his degree in 1925 days

### Part b

Time taken by a normal student to complete his/her degree = 3 x 365 + 366 days

= 1461 days

Additional time taken by John to complete the degree = 1925 - 1461 = 464 days

Hence, John took 464 more days to complete the degree than a normal student who completed his/her degree in time.

## Example 6

A car takes 395 minutes to complete a distance. Another car traveling at a different speed takes 150 more minutes to complete the same distance. How much time (in hours) is taken by the two cars to travel the same distance at different speeds?

### Solution

Let us label the cars as car A and car B.

Time taken by car A to cover the distance = 390 minutes

We have to convert minutes into hours. Since minutes is a smaller unit and hours is a bigger unit, hence we will use the arithmetic operation of division here for conversion.

Number of minutes in  one hour = 60 minutes

= hours

Hence, car A took 6.5 hours to cover the distance.

Time taken (in minutes) by Car B = 390 + 150 minutes

= 540 minutes

Number of minutes in an hour = 60

hours

Hence, car B took 9 hours to cover the same distance.

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