6. Time

By studying this lesson you will be able to

• identify months, years, decades, centuries and millenniums as units of time

• identify a leap year,

• identify the relationships between units of time, and

• add and subtract units of time.

6.1 Units of time

● Months and years

If we want to calculate the time taken for an event which commences on a particular date and ends on another date, in terms of days, weeks or months, we can do so by looking at a calendar.

A calendar is made up of the units days, weeks and months. You will see that there are 12 months in a calendar.

The calendar of year 2015 is shown below. The table shows the number of days in each month.

The calendar of a particular year provides information on a period of a year, starting from the first of January and ending on the thirty first of December of that year.

According to the year 2015 calendar, the total number of days in the year is 365. There are 365 days in a year which is not a leap year. We will be studying about leap years later.

👉The day 2015-08-01 means, the time period from 00:00 on 2015-08-01 to 24:00 on 2015-08-01.

👉The time at which a particular day ends ,is the time at which the next day starts. So the time 24:00 on 2015-08-01 is the same as the time 00:00 on 2015-08-02.

👉The year 2015 means, the time period from 00:00 on 2015-01-01 to 24:00 on 2015-12-31.

Note :

The international convention for measuring years is by considering the year of the birth of Jesus.

BC and AD are commonly used to count years in time. Jesus Christ’s birth is used as the starting point to count years that existed before (BC) and after (AD) he was born.

● Decades

A time period of ten years is considered as a decade. Let us consider 1948.

The first year in the decade that contains the year 1948 is 1941, and the last year in that decade is 1950.

The time period from AD 1 to AD 10 is called the first decade.

The time period from AD 11 to AD 20 is called the second decade.

The time period from AD 1811 to AD 1820 is called the hundred and eighty second decade.

The time period from AD 1951 to AD 1960 is called the hundred and ninety sixth decade.

The time period from AD 2011 to AD 2020 is called the two hundred and second decade.

That is, the time period from time 00:00 on 1941-01-01 to time 24:00

on 1950-12-31 is a decade. This decade is identified as the 195th decade.

● Centuries

A time period of a hundred years is called a century.

AD 1 to AD 100 is the first century.

AD 101 to AD 0200 is the second century.

AD 1801 to AD 1900 is the nineteenth century.

AD 1901 to AD 2000 is the twentieth century.

AD 2001 to AD 2100 is the twenty first century.

The time period from 00:00 on 2001-01-01 to 24:00 on 2100-12-31 is the twenty first century.

● A Millennium

A time period of a 1000 years is known as a millennium. According to the calendar, at this moment we are living in the third millennium.

The time period from AD 1 to 1000 is the first millennium.

The time period from AD 1001 to 2000 is the second millennium.

(1) Write down the decade to which each one of the following years belongs.

(i) AD 1856 

(ii) AD 1912 

(iii) AD 1978 

(iv) AD 2004

(2) Write the first date and the last date of the 22nd century.

(3) Write down the century to which each one of the following years belongs.

(i) AD 1796 

(ii) AD 1815 

(iii) AD 1956 

(iv) AD 2024

6.2 Leap year

The calendar of 2016 is given below. Consider the number of days ineach month . How does this differ from the calendar of 2015 ?

There are 29 days in the month of February. So the total number of days in 2016 is 366.

Any year in which there are 29 days in the month of February has 366 days in total. Such a year is defined as a leap year.

If a number that denotes a year is divisible by 4 but is not a multiple of 100, then that year is a leap year. However years which are denoted by numbers that are multiples of 100 become leap years only if they divisible by 400.

Note :

Any year which is not a multiple of 4 is not a leap year.

● Further units of time

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

There are months consisting of 28 days, 29 days, 30 days and 31 days.

However a time period of 30 days is considered as a month.

12 months = 1 year

365 days = 1 year

366 days = 1 leap year

A time period given in years can be represented in days, by multiplying it by 365.

A time period given in years can be represented in months, by multiplying it by 12.

Note :

We consider 30 days as a month. However, because a year consists of 12 months, you should not think that the number of days in a year is 360 (12 × 30 days). A year consists of 365 days.

(1) Choose the leap years from the years given below.

(i) AD 1896 (ii) AD 1958 (iii) AD 1960

(iv) AD 1400 (v) AD 1600 (vi) AD 2016

(2) 

(a) Indicate the days given below, in months and days.

(i) 225 days (ii) 100 days (iii) 180 days

(b) How many months are there in 5 years? How many days are there in 5 years?

(4) A patient has to take 3 tablets per day for a period of 2 months. How many tablets are required for this purpose?

(6) A person puts a minimum of 5 Rupees in a till every day. Find the least amount of money he would collect during each time period below.

(i) 6 months (ii) A leap year

6.3 Calculations related to time

A certain school was in session as follows during a certain year.

The first term consisted of 3 months and 6 days, the second term consisted of 3 months and 8 days, and the third term consisted of 3 months and 3 days.

Let us express the time period that the school was in session that year, in months and days.

For this we need to add the above time periods to find the total time period.

So the school was in session for 9 months and 17 days.

(3) 

Dileepa’s date of birth is 2003-09-07. 

Sithumini’s date of birth is 2000-02-04.

(i) Find how old Dileepa and Sithumini are today.

(ii) Find how much older Sithumini is to Dileepa,

(a) using their ages,

(b) using their dates of birth.

(4) Below are the service periods of two teachers in a certain school.

(i) Find the period of service of each teacher. Who has served longer in this school?

(ii) How many more years has the teacher has served than the other one ?

(5) Shashika’s date of birth is 2014-08-13. Aheli is 1 year, 8 months and 25 days older to her. What is Aheli’s date of birth?

(6) A school was opened on 1928-03-26.

(i) When is the school’s centennial anniversary?

(ii) How many days are there to the centennial anniversary date from today?

(7) Amila participated in Agricultural training progammes in Japan and China. He stayed in Japan from 2012-02-13 to 2014-07-27 and in China from 2014-12-17 to 2015-10-05. Find the total time he spent in Japan and China.

(1) A person borrows a certain amount of money. He has to pay the debt in equal installments once every month, for 10 years. The first installment was paid on 2016-01-01. Find the date on which he has to pay the final installment.

(2) Below are the age limits for participants in an inter-house sportsmeet of a certain school. 

Under 11 games – Age should be less than 11 years on 2016-03-31. 

Under 13 games – Age should be less than 13 years and greater than or equal to 11 years on 2016-03-31.

(3) 

Under 15 games – Age should be less than 15 years and greater than or equal to 13 years on 2016-03-31.

Under 17 games – Age should be less than 17 years and greater than or equal to 15 years on 2016-03-31.

The dates of birth of several students are given below.

Find which age group each student qualifies to participate in.