Time: Representation and Conversions

Time: Every morning, we have to plan our day; we go to school, have our lunch break, play with our friends, etc. Even our parents have a schedule for the day. Knowing how to manage your time is the only way you can do these things. In ancient times, people used to keep track of time by looking at the movements of the sun and the phases of the moon. One of the first clocks mankind invented to measure time was a sundial which was invented around 1500 BC. However, technological growth allowed us to develop clocks that is used to measure the exact time across the globe.

The first thing you should know about clocks is that each number on a clock represents an hour. When the hands rotate from 1 to 12, the time is labeled AM. Morning hours are marked with AM. The second rotation of the hands from 1 to 12 is labeled PM. This indicates the afternoon, evening, and night hours. In this article, we will discuss time, how to read clocks and the concept of AM and PM.

What is Time?

Time is a beneficial concept that we use in our day-to-day life. We need to keep track of when we cook, play, study, go to school, meet someone, etc. So, having proper knowledge about time is very important. Generally, time is an answer to when the specific event will happen or has happened.

The term time defines when a specific event happens, has happened, or happens. Time is the measurable quantity and is also infinite. Time is calculated in seconds, minutes, hours, days, months, and years. 

You can also see that there are smaller time units, like milliseconds and microseconds. And the smallest time unit is ‘Zeptosecond.’ It is also essential to know the various times of the day before moving to the concept of reading and measuring time.

A.M. and P.M.

The time displayed on the clock from \(12\) midnight to \(11: 59\) in the morning is referred to as \(\text {A.M.}\)

The time displayed on the clock from noon to late-night at \(11: 59\) is referred to as \(\text {P.M.}\)

Reading and Representation of Time

The frequently used phrase by many of us is “please be there on time”. As we all know, managing time is a crucial quality to organize your work and be a successful person. So, to be punctual and manage time well, you need to have a good understanding of time.

Measurement of Time Using Clocks

We have three hands on the clock, and the largest unit of time is an hour. The day has \(24\) hours whereas a clock has the numbers only from \(1\) to \(12\) written on it. This indicates that there will be two rounds of \(12\) hours in a day.

You can see on the clock there are \(12\) sections. Each of the numbers represents an hour. There are three hands. The longer hand is the minute hand, the shorter hand is the hour hand, and the thin longhand is the second’s hand. Each indicator points to a number, and the combination of the hour, minute, and seconds hand together tells us the time.

Short Hand or Hour Hand: The small needle representing the hour is known as the shorthand or hour hand.

Longer Hand or Minute Hand: The long needle representing the minutes is known as the minute hand or longhand.

Seconds Hand: The long and thin needle which represents the seconds is known as the second’s hand.

The minute lines shown between each number represent the minute. In between any two numbers on the clock, you have \(5\) minutes. So, the minute starts from \(0\) at number \(12\), and the count goes on till the number \(60\). Look at the example of the clock shown below:

You can see that the hour hand points at \(3\) and the minute hand points at \(12\). So, the time in the above clock is \(03: 00\) or \(3\)’O clock.

You can see the time measurement for \(15\) minutes, \(30\) minutes, and \(45\) minutes are displayed below:

Quarter to: This term refers to that \(15\) minutes are left to complete the given hour.
Example: The given time \(06: 45\) means still you have \(15\) minutes to reach \(7: 00\), which is read as “a quarter to seven”.

Quarter past: This term refers that \(15\) minutes that have passed after the hour has begun.
Example: The given time, \(08: 15\), means \(15\) minutes have been passed since \(8: 00\), which is read as “a quarter past eight”.

Half-past: This term refers that \(30\) minutes that have passed after the hour has begun.
Example: The given time, \(09: 30\) means \(30\) minutes have been past \(9: 00\), read as “half-past nine”.

Represent Time in 12 Hours Clock and 24 Hours Clock

You know that there are two types of clocks: a \(12\) – hour clock and a \(24\) – hour clock. The time from \(12\) midnight to \(12\) noon is expressed as \(\text {a.m.}\), while \(12\) noon to midnight is expressed as \(\text {p.m.}\)

The format of a \(24\) – hour clock is hours: minutes or minutes: seconds.

We have already learned the given conversions of days, hours, and minutes.

\(1\) day \(=24\) hours
\(1\) hour \(=60\) minutes
\(1\) minute \(=60\) seconds
\(7\) days \(=1\) week
\(1\) year \(=365\) or \(366\) days (in case of leap year)

Conversion of Days to Hours and Vice Versa

We can convert days to hours and hours to days as given below:

\(1\) day \(=24\) hours \((h)\) and \(1\) hour \((h)=\frac{1}{24}\) day

To convert days and hours to hours, multiply the given days by \(24\) and add the additional hours.

To convert hours to days and hours, divide the given hours by \(24\). Write the quotient obtained as the number of days and the remainder as the number of hours.

Example: Convert \(5\) days into hours.

You have to multiply the number of days by \(24\).

So, multiply \(5\) days \(=5 \times 24\) hours \(=120\) hours.

Conversion of Hours to Minutes and Vice Versa

We can convert hours to minutes and minutes to hours as shown below:

\(1\) hour \((h)=60\) minutes \((\mathrm{min})\) and \(1\) minute \((\mathrm{min})=\frac{1}{60}\) hours \((h)\)

To convert hours and minutes to minutes, multiply the given hours with the number \(60\) and add the allotted minutes to it.

To convert the minutes to hours and minutes, divide the given minutes by \(60\). Write the quotient obtained as the number of hours and the remainder as the number of minutes.

Example 1: Convert \(12\) hours \(15\) minutes to minutes.
\(12\) hours \(15\) minutes \(=(12 \times 60)\) minutes \(+15\) minutes
\(=720\) minutes \(+15\) minutes \(=735\) minutes

Example 2: Convert \(465\) minutes to hours and minutes.
\(465\) minutes \(=\frac{465}{60}\) (since \(1\) minute \(=\frac{1}{60}\) hour)
\(=7\) hours \(45\) minutes

Conversion of Minutes to Seconds and Vice Versa

We can convert minutes to seconds and seconds to minutes as shown below:

\(1\) minute \((\mathrm{min})=60\) seconds \((\mathrm{s})\) and \(1\) second \((\mathrm{s})=\frac{1}{60}\) minute \((\mathrm{min})\)
To convert minutes and seconds to seconds, multiply the given minutes by \(60\) and add the given seconds.

To convert seconds to minutes and seconds, divide the given seconds by \(60\). Write the quotient obtained as the number of minutes and the remainder as the number of seconds.

Example 1: Convert \(240\) minutes to seconds.

\(240\) minutes \(=240 \times 60\) seconds \(=14,400\) seconds.

Example 2: Convert \(3,600\) seconds to minutes.

\(3,600\) seconds \(=\frac{3600}{60}\) minutes \(=60\) minutes.

Solved Examples

Q.1. Convert \(7\) days \(14\) hours to hours.
Ans: We have \(7\) days \(14\) hours
So, we will multiply the number of days with the number \(24\) and then add the number of hours given.
Now, \(7\) days \(14\) hours \(=(7 \times 24)\) hours \(+14\) hours
\(=168\) hours \(+14\) hours \(182\) hours
Hence, the required answer is \(182\) hours.

Q.2. Convert \(640\) hours to days and hours.
Ans: We have \(640\) hours
Now, convert the given hours into days and hours.
So, we divide the numbers \(640\) hours \(=\frac{640}{24}\) (since \(1\) hour \(=\frac{1}{24}\) day)
\(=26\) days and \(16\) hours.
Hence, the required answer is given above.

Q.3. Convert \(14\) hours \(13\) minutes to minutes.
Ans: We have \(14\) hours \(13\) minutes
So, multiply the given hours with the number \(60\) and add the given minutes to it.
Now, \(14\) hours \(13\) minutes \(=(14 \times 60)\) minutes \(+13\) minutes
\(=840\) minutes \(+13\) minutes \(=853\) minutes

Q.4. Convert \(450\) minutes to hours and minutes.
Ans: We have \(450\) minutes
So, divide the given minutes by \(60\). Write the quotient obtained as the number of hours and the remainder as the number of minutes.
Now, \(450\) minutes \(=\frac{450}{60}\) (since \(1\) minute \(=\frac{1}{60}\) hour)
\(=7\) hours \(30\) minutes

Q.5. Covert \(540\) minutes to seconds.
Ans: We have \(540\) minutes
So, we will multiply the given minutes by \(60\) and add the given seconds to it.
Now, \(540\) minutes \(=540 \times 60\) seconds \(=32,400\) seconds.
Hence, the required answer is \(32,400\) seconds.

Summary

In this article, we have discussed the time, then what do \(\text {a.m}\) and \(\text {p.m}\). mean. Then, we talked about reading and representation of time, which covered the reading time from the clock, shorthand, and longhand followed by quarter to, quarter past, and half past. Finally, we glanced at the representation of \(12\) hour and \(24\) – hour clocks, including the conversions of days to hours, hours to minutes, and minutes to seconds, and then we have given solved examples along with a few FAQs..

FAQs About Time

Let’s look at some of the commonly asked questions about time:

Q.1. Who invented time?
Ans: The person named Christiaan Huygens is usually credited as the inventor of the time. He determined the mathematical formula related to pendulum length to time (about \(99.4 \mathrm{~cm}\) or \(39.1 \,\text {inches}\) for the one-second movement) and had the first pendulum-driven clock made.

Q.2. What is the definition of time in math? 
Ans: The term time defines when a specific event happens, has happened, or happens. Time is the measurable quantity and is also infinite. Time is measured in seconds, minutes, hours, days, months, and years.

Q.3. How do you subtract time in math?
Ans: When you want to subtract the time, you have to arrange the hours, minutes, and seconds vertically and then subtract as shown below:
Example: Subtract \(8 \,h\, 3829\, s\) from \(10\, h\, 4939\, s\)

So, \(8 \,h\, 3829\, s-10\, h\, 4939\, s=2\, h\, 1110\, s\)

Q.4. How to read a clock?
Ans: You can see on the clock there are \(12\) sections. Each of the numbers represents an hour. There are three hands. The longer hand is the minute hand, the shorter hand is the hour hand, and the thin longhand is the second’s hand. Each indicator points to a number, and the combination of the hour, minute, and seconds hand together tells us the time.
You can see below the given clock shows the time as \(2:30\).

Q.5. How do you add time in math?
Ans: When you want to add the time, you have to arrange the hours, minutes, and seconds vertically and then add as shown below:
Example: Add \(3 \,h\, 3830 \,s\) from \(5\, h\, 2012\, s\)

So,  \(3\, h \,3830\, s + 5 \,h\, 2012\, s =8\, h\, 5842\, s\)

We hope this detailed article on the concept of time in maths helped you in your studies. If you have any doubts or queries, you can reach out to us through the comment section and we will help you at the earliest.