**Introduction**

We are aware of the clocks we use every day in our life to check time. There are calendars that tell us which day of the year is it? How do you answer when someone asks you, “ What is the time? “ definitely, you will check the time from the clock, be it the one you are wearing, on the time being displayed on your phone, or through the wall clock. They all tell time but maybe in different formats. So, how do we these different measures of time? Let us find out.

Time is not a new concept. Since ancient times, our ancestors have been measuring time starting with the calculations based on the movement of the sun and the moon. As the sun moves across the sky, shadows change in direction and length, so a simple sundial can measure the length of a day. It was quickly noticed that the length of the day varies at different times of the year. Gradually, with the advent of modern inventions and theories, the concept of time that we know today evolved.

**What is Time?**

Time can be defined as the dimension based on which the evolution of any system takes place. We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars. Let us learn about these one by one.

**Understanding Time**

Time is measured in hours, minutes and seconds. How are these three related to each other?

**1 minute = 60 seconds**

**1 hour = 60 minutes**

This means that 1 hour = 60 x 60 = 3600 seconds

A second is a very short period of time, say the time that is taken to blink your eye, to snap your fingers etc. it is a smaller unit of time than a minute.

**Understanding the Clock**

We see different types of clocks everywhere around us. But do we define a clock? A clock is an instrument to measure time which is shown in hours, minutes and seconds. There are two types of clocks –

**Analog Clock – **Analog clocks are the clocks that use hands to show us the hours, minutes and seconds are called analog clocks. There are two hands in the analog clocks –

The little hand shows the hour.

The bigger hand shows the minutes.

In many clocks there is another big constantly moving hand that shows the seconds.

**Digital Clock – **Digital Clocks are the clocks that use numbers to show the hours and minutes such as 5:35.

Consider the clock shown above. We can see that there is a short hand at 5 which represents the hour, while the bigger hand at 3 represents the minutes. So, the time is 5 hours and 15 minutes. How did we get that time? Let us find out.

**Telling Time to Exact Minute**

To understand how to tell time to exact minute, let us consider an example.

Suppose Victor and his sister Alice were going to school. When they started from home, the following time was shown by the clock –

Victor asked her to read the time. She read it easily as 7:30. Then they reached the school and the time shown by the clock in the school is

Victor again asked her to read the time. But, she was not able to read the time to the exact minutes. Now, Victor told her it was 8: 10. Let us understand how to read time to exact minutes.

If you see carefully, there are 12 numbers and 60 divisions on the face of a clock. Therefore, we have,

1 hour = 60 minutes.

Hence, the number of divisions between two consecutive numbers is 60 ÷ 12 = 5 divisions or 5 minutes.

We will read the time on the given clock as 2 :07 if,

- The hour hand of the clock is at 2
- The minute hand of the clock is at the 2nd division after the 1
^{st}number, i..e 7 minutes ( 1 x 5 = 5) + 2 minutes = 7 minutes.

Hence, we can say that the numbers on the clock actually represent hours and the divisions between them represent the minutes.

It is important to know here that –

**Quarter of an hour = 60 ÷ 4 = 15 minutes**

**Half of an hour = 60 ÷ 2 = 30 minutes.**

**12 :00 o’clock in the night is 12:00 midnight**

**12 :00 o’clock at the daytime is 12:00 noon**

**We do not write a.m. or p.m. with 12:00 o’clock time.**

**In what time to the hour, minute and second hands complete one round or one revolution of the clock? **

- The hour hand of the clock goes round the clock in 12 hours.
- The minute hand completes one round in 1 hour.
- The second’s hand completes one round in 1 minute

**Third Hand of a Clock**

Many of the clocks have three hands instead of two. What is this third hand for? The third hand is usually long and thin, and it is called the second hand. The seconds hand takes 60 seconds to complete one round of the clock.

Therefore, 1 minute = 60 seconds.

Hence the second hand is a smaller unit of time than a minute.

Thus, second is the smallest unit and hour is the largest unit among the three units of time i.e. hour, minute and second.

When the second hand moves once around the clock the minute hand moves through 1 minute

Now, it should be noticed that at times we see time marked in a.m. and p.m. What do we mean by a.m. and p.m.? Let us find out.

**Time in a.m. and p.m.**

We can observe that there are 12 numbers written on the face of a clock. We also know that a day has 24 hours. Therefore, the hour hand of the clock completes 1 round in 12 hours. So, we divide 24 hours of a day in two periods:

- From 12:00 midnight to 12:00 noon
- From 12:00 noon to 12:00 midnight

**The time between 12:00 midnight to 12:00 noon is written as a.m. Here a.m. means ante meridiem which means before midday.**

**The time between 12:00 noon and 12:00 midnight is known as p.m. Here p.m. means post meridiem which means after midday. **

Another thing that should be noticed is that at times we see time written in a.m. or p.m. while at times it is written as, say, 16:00 with no mention of a.m. and p.m. What is this time and how is it written? Let us find out.

**12-hour Clock vs 24-hour Clock**

There are two ways of telling the time:

The 12-hour clock runs from 1am to 12 noon and then from 1pm to 12 midnight.

The 24-hour clock uses the numbers 00:00 to 23:59 (midnight is 00:00).

Let us do a time comparison between the two styles of telling time.

12-hour Clock | 24-hour Clock |

1 : 00 am | 1 : 00 |

2 : 00 am | 2 : 00 |

3 : 00 am | 3 : 00 |

4 : 00 am | 4 : 00 |

5 : 00 am | 5 : 00 |

6 : 00 am | 6 : 00 |

7 : 00 am | 7 : 00 |

8 : 00 am | 8 : 00 |

9 : 00 am | 9 : 00 |

10 : 00 am | 10 : 00 |

11 : 00 am | 11 : 00 |

12 : 00 noon | 12 : 00 |

1 : 00 pm | 13 : 00 |

2 : 00 pm | 14 : 00 |

3 : 00 pm | 15 : 00 |

4 : 00 pm | 16 : 00 |

5 : 00 pm | 17 : 00 |

6 : 00 pm | 18 : 00 |

7 : 00 pm | 19 : 00 |

8 : 00 pm | 20 : 00 |

9 : 00 pm | 21 : 00 |

10 : 00 pm | 22 : 00 |

11 : 00 pm | 23 : 00 |

12 : 00 midnight | 24 : 00 |

Now that we have understood time, let us move to understand the days, weeks, months and years.

**The Calendar**

Observe the calendar carefully. You will see that the calendar has 12 months. Let us learn more about these months.

Let us start from a day. We have learnt about time and know that there are 24 hours in a day. So, we have,

1 day = 24 hours

1 week = 7 days

1 month = 30 / 31 days

1 years = 365 days

1 leap year = 366 days.

Let us learn more about them

**Days, Weeks, Months and Years**

A day comprises from 12:00 midnight of one day to 12:00 midnight of the next day which is equal to 24 hours. There are different days that fall in the order –

**Monday**

**Tuesday**

**Wednesday**

**Thursday**

**Friday**

**Saturday**

**Sunday**

These 7 days together comprise one week. Therefore,

**1 week = 7 days**

**The following is the representation of a week in a month.**

There are 12 months in a year. But every month does not have the same number of days. The following are the months and the number of days each month has –

Name of the Month | Number of days |

January | 31 |

February | 28 or 29 |

March | 31 |

April | 30 |

May | 31 |

June | 30 |

July | 31 |

August | 31 |

September | 30 |

October | 31 |

November | 30 |

December | 31 |

We can see above the month of February has either 28 days or 29 days. How do we decide in which year February has 28 days and in which year it has 29 days? This is where the concept of leap year comes in. So, what is leap year?

**Leap Year **

We know that a year has 364 days. However, in actual it has 365$\frac{1}{4}$ days. This $\frac{1}{4}$ days or the quarter of a day is added every four years to make one full day. Hence, every fourth year we have 366 days in a year instead of 365 days. This additional one day is added to the month of February which otherwise has 28 days. So, in this year the month of February has 29 days and it is called a leap year. How do we know which is this fourth year that forms the leap year? We can simply check by dividing the year by 4. If it is divisible by 4, then the year is a leap year.

Therefore, we can say that –

**Year**** ****Number of days**

2020 366 – Leap Year

2021 365 days

2022 365 days

2023 365 days

2024 366 days – Leap Year

Hence, we can see that after every 4 years we have a leap year in which the month of February has 29 days.

**Solved Examples**

**Example 1** Change the 24-hour clock time to 12-hour clock time

a) 11 : 15 hours

b) 16 : 40 hours

**Solution** We have been given time in 24-hour clock and we need to change it into 12-hour clock. Let us do them one by one.

a) 11 : 15 hours

We know that 11 : 00 in 12 hour format means 11 : 00 am. **Therefore 11 : 15 hours in 12 hour format will mean 11 : 15 a.m.**

b) We have been given 16 : 40 hours.

Now, 16 = 12 + 4

Therefore, 16 : 00 hours = 4 : 00 p.m.

**Hence, 16 : 40 hours = 4 : 40 p.m.**

**Example 2** Alice’s school closed for the summer vacations on 4 May and reopened on 16 June. For how many days the school close for the summer vacations?

**Solution** We have bene given that Alice’s school closed for the summer vacations on 4 May and reopened on 16 June. Now, since Alice’s summer vacations began on 4 May, so she would not go to school on 4 May. Therefore, we will include 4 May as vacation. Also, we know that the month of May as 31 days. Therefore, we have,

Number of vacation days in the month of May = 31 – 3 = 28 days ……. ( 1 )

Now, we have been given that the school reopened on 16 June. This means that Alice went to school on 16 June. Therefore, 16 June will not be included in the vacation days. Hence, we have,

Number of vacation days in the month of June = 25 days ………………. ( 2 )

Now, to obtain the total number of vacation days we need to find the sum of ( 1 ) and ( 2 ). Therefore, we have,

Total number of vacation days = 28 + 15 = 43 days.

**Hence, the school was closed for 43 days for the summer vacations. **

**Example 3**** **What was the date on 27 days after 13 February 2014 ?

**Solution** We know that 2014 was not a leap year. This means that in 2014 the month of February had 28 days.

Hence the number of days to be considered in the month of February = 28 – 13 = 15 days.

We are required to find the date 27 days after 13 February. Now, out of these 27 days, 15 days are consumed in February. Therefore we are left with 27 – 15 = 12 days which need to be forwarded to the next month which is March. Therefore, we have

The date which was 27 days after 13 February 2014 = 12 Mach 2014.

**Key Facts and Summary**

- Time can be defined as the dimension based on which the evolution of any system takes place.
- A second is a very short period of time, say time taken to blink your eye, to snap your fingers etc.
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- A clock is an instrument to measure time which is shown in hours, minutes and seconds.
- Quarter of an hour = 60 ÷ 4 = 15 minutes
- Half of an hour = 60 ÷ 2 = 30 minutes.
- 12 :00 o’clock in the night is 12:00 midnight
- 12 :00 o’clock in the daytime is 12:00 noon
- We do not write a.m. or p.m. with 12:00 o’clock time.
- The numbers on the clock actually represent hours and the divisions between them represent the minutes.
- Second is the smallest unit and hour is the largest unit among the three units of time i.e. hour, minute and second. When the second hand moves once around the clock the minute hand moves through 1 minute
- The time between 12:00 midnight to 12:00 noon is written as a.m. Here a.m. means ante meridiem which means before midday.
- The time between 12:00 noon and 12:00 midnight is known as p.m. Here p.m. means post meridiem which means after midday.
- The hour hand of the clock goes round the clock in 12 hours.
- The minute hand completes one round in 1 hour.
- The second’s hand completes one round in 1 minute
- After every 4 years, we have a leap year in which the month of February has 29 days.
- There are two ways of telling the time, the 12-hour clock runs from 1am to 12 noon and then from 1pm to 12 midnight and the 24-hour clock uses the numbers 00:00 to 23:59 (midnight is 00:00).