Measurement

Introduction:

The basic metric units are Metre, Litre, Gram, Seconds and so on. It is based on the decimal system (10), which is easier to convert from one unit to another. we use kilometre, meter, centimetre, millimetre to measure length; kilogram, gram, milligram for weight and kilolitre, litre, millilitre for volume in shops, schools, office, railways, and many other places. An eye blink represents a second; heartbeats are counted per minute; the working time of an employee is calculated in hours.

Basic metric units are: Length in the meter. Weight in gram. Capacity (volume) in litre.

We use different metric units for different sizes in various situations

Size	Metric Units
Large ones	kilometre / kilolitre/ kilogram
Medium ones	meter/litre/gram
Small ones	centimetre/centilitre/centigram
Very small ones	millimetre/millilitre/milligram

While knowing the different units used in the metric system is important, the real purpose behind learning the metric system is for you to be able to use these measurement units to calculate the size, mass, or volume of different objects. In practice, it is often necessary to convert one metric measurement to another unit—this happens frequently in the medical, scientific, and technical fields, where the metric system is commonly used. 

Metric unit table:

For length	kilometre(km)	hectometre(hm)	decametre(dam)	Meter(m)	decimetre(dm)	centimetre(cm)	millimetre(mm)
For weight	kilogram(kg)	hectogram9hg)	decagram(dag)	gram(g)	decigram(dg)	centigram(cg)	milligram(mg)
For volume	kilolitre(kl)	hectolitre(hl)	decilitre(dal)	litter(l)	decilitre(dl)	Centilitre(cl)	millilitre(ml)

Conversions within the Metric system:

All units of length in the metric system are defined in terms of the metre. A prefix is added to indicate the decimal place value position of the measurements. Similarly the units of weight and volume are defined in terms of gram and litre respectively. Let us observe the conversion chart.

(i) When we move from higher unit to lower unit, multiply the given measure by the powers of 10’s.

(ii) When we move from lower unit to higher unit, divide the given measure by the powers of 10’s.

Conversion Table:

Length	Weight	volume
1 km = 1000m	1 kg = 1000 g	1 kl = 1000 l
1 m = 100 cm	1 g = 1000 mg	1 l = 1000 ml
1 m = 1000 mm
1 cm = 10 mm

Example: The average rainfall of Tamil Nadu is 998 mm. convert it into cm.

Solution:

The average rainfall = 998 mm =998*cm [1 cm = 10 mm]

= 99.8 cm.

Example: Janaki bought 650 mg of a tablet. : hat is its weight in gram"

Solution:

Weight of a tablet = 650 mg = 650*g [1 g = 1000 mg]

= 0.65 g.

Problem for you:

i) 23 km into m

ii) 7814 m into km

iii) 8.67 mm into cm

iv) 16 l into ml

v) 1500 ml into l

vi) 2360 l into kl

vii) 873 l into ml

viii) 40 mg into g

ix) 1550g into kg

Fundamental operation on Quantities:

We can do the basic operations on the metric units as we do the decimal operations.

Note that, measurements with the same unit can be added/ subtracted, but unlike units of measurements should be converted into like units and then they can be added / subtracted.

Example:

Pradeep travels 4 km and 350 m to reach to the market, while kandan travels 6 km and 200 m to reach to the same market from their houses. How much distance does kandan travel more than Pradeep?

Solution:

Distance travelled by kandan =6 km 200m =6*1000 m +200 m = 6200 m

Distance travelled by Pradeep = 4 km and 350 m =4*1000 m + 350 m = 4350 m

Difference in distance of their travel = 6200 – 4350 =1850 m

Kandan travelled 1 km and 850 mm more than Pradeep.

Problem based on above concept:

1. Fill in the blanks

(i) 250 ml +l = ……………… l

(ii) 150 kg 200 g + 55 kg 750 g =……kg ………g

(iii) 20 l – 1 l 500 ml = ………l ………ml

(iv) 450 ml x 5 =……. l …… ml

(v) 50 kg ÷ 100 g =…….

Answers:

(i) 750 ml

(ii) 205 kg and 950 g

(iii) 18 l and 500 ml

(iv) 2 l and 250 ml

(v) 500 g

2. Convert into higher units: (i) 13000 mm (km, m, cm) (ii) 8257 ml (kl, l)

Solution:

(i) 13000 mm = 13 m = 0.013 km.

(ii) 8257 ml = 8.257 l = 8.257*10^-3 kl.

3. Convert into lower units: (i) 15 km (m, cm, mm) (ii) 12 kg (g, mg)

Solution:

(i) 15 km = 15*1000 m = 15000 m = 15*10⁶ mm.

(ii) 12 kg = 12000 g = 12*10⁶ mg.

4. Compare and put >or< or = in the following:

(i) 800 g + 150 g 1 kg

(ii) 600 ml+400 ml 1 l

(iii) 6 m 25 cm 600 cm+25 cm

(iv) 88 cm 8 m 8 cm

(v) 55 g 550 mg

Solution:

(i) < (ii) < (iii) = (iv) < (v) >

5. Geetha brought 2 l and 250 ml of water in a bottle. Her friend drank 300 ml from it. How much of water is remaining in the bottle?

Solution:

Geeta have 2 l and 250 ml = 2*1000+250 ml = 2250 ml.

Her friend drank 300 ml from it.

Water remaining in the bottle = 2250 – 300 = 1950 ml.

6. In a school, 200 litres of lemon juice is prepared. If 250 ml lemon juice is given to each student, how many students get the juice?

Solution:

Total lemon juice is prepared in a school is 200 l = 200*1000 l = 200000 l.

If each student is given 250 ml of juice.

Then, total no of student get the juice is 200000/250 ml = 800 students.

Measurement of time:

The teacher asks students to answer the following questions:

How long do you take to run 100 metres?

How long do you take to walk one kilometre?

What is the time taken for a cup of rice to be cooked?

What is the cultivation period of groundnut?

These questions will help us to find the importance of time in our day-to-day life. Now let us discuss the development of measures of time.

Time taken by the Earth to complete one full rotation around the Sun is known as the Solar Year. It was divided into 12 equal parts which is known as the Solar month. The duration between two full moons is known as the lunar month and 12 lunar months are known as lunar year. But we follow solar year and month.

We know that the measurement of time is read by a clock or a watch. Any clock or watch except a digital watch, has a dial. On the circular border of the dial of a watch or clock there are the hour numbers from 1 to 12 at equal intervals. Between the two numbers there are five divisions. Each division represents a minute. There are two hands of different lengths having one of the ends fixed at the centre of the dial. The small hand is the hour hand and longer hand is the minute hand. The hour-hand moves slower than the minute hand. There is also a third hand called the second-hand. It moves very fast.

The hour hand makes one round of the dial in 12 hours. It moves from one number to its nearest number in one hour, i.e., the hour hand goes from 12 to 1 or 1 to 2 or 2 to 3, etc., in one hour.

The minute hand makes one round of the dial in 1 hour. It moves across one division in one minute or five divisions in 5 minutes.

If there is a second-hand, it makes one round of the dial in one minute, i.e. it moves across one division in one second.

Unit of Time:

Today we are measuring time accurately. The units of time are second, minute, hour, day, week, month, year, etc. They are interrelated.

On this basis we say:
1 hour = 60 minutes or 60 minutes = 1 hour
1 minute = 60 seconds or 60 seconds = 1 minute
1 hour = 60 minutes = 60*60 seconds or 3600 seconds

1 day= 24 hours or 1 week = 7 days =24*7 = 168 hours

1 months = 30 days = 30*24 hours = 720 hours

1 year = 365 days = 365*24 = 8760 hours.

Practise to say time in two ways:-

(i) When the minute hand is on the left hand side of the clock, (from 6 hours to 12 hours) we read the time as __ minute to ___hour.

Example: 20 min to 10.

(ii) When the minute hand is on the right hand side of the clock.(from 12 hours to 6 hours) we read the time as __ minute past ___hour.

Example: 25 min past 4.

Conversion of Time:

Calculation of time to the nearest seconds is very essential in some situations like launching rocket, running race, arrival and departure. So, we need to know the conversion of time.

Example:

A farmer ploughed the paddy field for 3 hours 35 minutes. How many minutes did he plough?

Solution:

Time for which the farmer ploughed the paddy field = 3 hours and 35 minutes

= 3 * 60 minutes + 35 minutes = 180 minutes + 35 minutes

= 215 minutes.

Example:

A satellite is placed in its orbit in 7 hours 16 minutes 20 seconds. Calculate it in seconds. Solution: The satellite reaches its orbit in 7 hours + 16 minutes + 20 seconds

= (7*60*60) seconds + (16 * 60) seconds +20 seconds

= 25200 seconds + 960 seconds + 20 seconds = 26,180 seconds.

The satellite reaches its orbit in 26,180 seconds.

Ordinary Time or the 12-Hour Format:

The 12 hour clock has antemeridian (am) and postmeridian (p.m.) because the number of hours in a day is divided into day and night. In the clock, exactly 12.00 at night is called midnight; and exactly 12.00 at day is called noon.

a.m. (antemeridian) denotes the time that is after 12:00 midnight and before 12:00 noon.

p.m. (postmeridian) denotes the time that is after 12:00 noon and before 12:00 midnight.

Example: Morning 5 o’ clock is denoted as 5.00 a.m.

Evening 5 o’ clock is denoted as 5.00 p.m.

In 3.20 a.m., the point does not mean the usual decimal point.

Railway Time or the 24-Hour Format:

Generally, we use 12 hour clock but Railways, Airways, Defence forces and Television networks use 24 hour clock to avoid morning or evening confusions. : When you are in a railway station, you can hear the announcement and see the use of hours instead of a.m. and p.m, because they follow the 24 hour format. Therefore, there is no need to say morning and evening in their time. Railway time is usually denoted in 4 digits. The first two digits shows the hours and the last two digits shows the minutes. For example, 5 pm is denoted as 17:00 hours.

Example:

7 o’ clock morning = 07:00 hours.

1 o’ clock evening = 13:00 hours (12+1 hour).

i.e., after 12 noon they count continuously up to 24 hours.

12 midnight is written as 00:00 hours or 24:00 hours.

12 noon is written as 12:00 hours.

Conversion of Time Formats:

Let us observe the clock. Remember the following points while converting from one type of time to another type:

To convert 12 hour time to 24 hour time, simply change 12 hours as 00:00 hours between 12.00 midnight and 01.00 a.m. there is no change up to 01.00 p.m. Add 12:00 hours to any hour from 01.00 p.m.

To convert 24 hour time to 12 hour time simply change 00:00 hours as 12 hours between 00:00 hours and 01:00 hour. There is no change up to 13:00 hours. Subtract 12:00 hours from any hours from 13:00 hours. Minutes will not change in both the formats.

Convert into the 12 hour format: (Ordinary time):

24 hour format	>12 hour	If. 12 hour then subtract 12	12 hour format
09:25 hours	no	-	9.25 a.m.
18:40 hours	yes	18-12=6	6.40 p.m.
03:15 hours	no	-	3.15 a.m.
15:30 hours	yes	15-12=3	3.30 p.m.
23:50 hours	yes	23-12=11	11.50 p.m.

Convert into the 24 hour format (Railway time);

12 hours time	a.m. / p.m.	Add 12 to p.m.	24 hour format
04:15 a.m.	a.m.	-	04:15 hours
07:40 p.m.	p.m.	7+12 hours	19:40 hours
10:05 p.m.	p.m.	10+12 hours	22:05 hours
06:00 a.m.	a.m.	-	06:00 hours
12:25 a.m.	a.m.	-	00:25 hours

Example: Convert the 12 hour format into the 24 hour format and vice versa:

10.40 a.m. = 10:40 hours	1 p.m. = 13:00 hours
1.15 a.m. = ______ hours 1	3 p.m. = _______ hours
5 a.m. = ________ hours	12 midnight = ______ hours
16:20 hours = ______a.m./p.m.	12:25 hours = ______a.m./p.m.

Duration between the two given time instances:

Example: Find the duration between 6 a.m. and 4 p.m.

Solution:

Conversion of 6 a.m. to Railway time = 06:00 hours

Conversion of 4 p.m. to Railway time = (4+12) hours = 16:00 hours

Time duration between 6 a.m. and 4 p.m.

= The difference between 16 hours and 6 hours = 16 hours and 6 hours = 10 hours.

Year:

A year is the time taken by the Earth to make one revolution around the Sun. A year has 12 months or 365 days. Each month is divided into weeks. A month has 4 weeks and a few more days. A week is of 7 days. A month has 30 days / 31 days except February. February has 28 or 29 days.

Leap Year:

We know that the Earth revolves around the Sun as well as rotates to itself. The Earth takes 365 days 6 hours to make a complete revolution around the sun. We take 365 days as one year. To adjust 6 hours each year, we add one day to every fourth year (4 years î 6 hours = 24 hours = 1 day). Every 4th year has 365 +1 day = 366 days and one day is added to the month of February. Therefore a year which has 366 days is called a Leap Year. In a Leap Year the month of February has 29 days. Every year you are celebrating birthday. If a person s birthday falls on 29th February, he/she has to celebrate the birthday once in 4 years only.

How can we identify a leap year?

So, Generally a year which is divisible by 4 is considered as a leap year.

Examples:

1. 2016 is a leap year, because 2016 is exactly divisible by 4.

2. 2018 is not divisible by 4 and it leaves remainder. So it is not a leap year.

In centuries:

Years which are multiples of 100 are centuries, such as 1100, 1200, 1300….1900, 2000, 2100 ….etc. The century which is divisible by 400 is a leap year.

Examples:

1. 1200 is divisible by 400; and so it is a leap year.

2. 1700 is not divisible by 400 and so it is not a leap year.

Questions:

1. Check whether the following years are Ordinary or Leap Year (1994; 1985; 2000; 2007; 2010; 2100)?

Solution:

Ordinary year: 1994, 1985, 2007, 2010.

Leap year: 2000, 2100.

2. How many days are there from 1st April to 30th -June?

Solution:

There are 91 days from 1^st April to 30^th June.

Problem based on above concept:

1. Convert the following:

(i) 20 minutes into seconds.

(ii) 5 hours 35 minutes 40 seconds into seconds.

(iii) 580 minutes into hours.

(iv) 25200 seconds into hour.

Solution: (i) 1200 seconds.

(ii) 1, 62, 18,000 seconds.

(iii) 9.6 hours.

(iv) 7 hours.

2. The duration of electricity consumed by the farmer for his pump-set on Monday and Tuesday was 7 hours 20 minutes 35 seconds and 3 hours 44 minutes 50 seconds respectively. Find the total duration of consumption of electricity?

Solution:

Electricity consumed on Monday is 7 hours 20 minutes 35 seconds

Electricity consumed on Tuesday is 3 hours 4 minutes 50 seconds

Total duration of time is 7 hours 20 minutes 35 seconds + 3 hours 44 minutes 50 seconds

= 11 hours 5 minute 25 seconds.

3. Change the following into 12 hour format:

(i) 02:00 hours

(ii) 08:45 hours

(iii) 21:10 hours

(iv) 11:20 hours

(v) 00:00 hours

Solution:

(i) 2 a.m.

(ii) 08:45 a.m.

(iii) 09:10 p.m.

(iv) 11:20 a.m.

(v) Midnight i.e. 00:00 a.m.

4. Calculate the duration of time:

(i) From 5.30 a.m. to 12.40 p.m.

(ii) From 1.30 p.m. to 10.25 p.m.

(iii) From 20:00 hours to 4:00 hours

(iv) From 17:00 hours to 5:15 hours

Solution:

(i) 7 hours 10 minute.
(ii) 9 hours 55 minutes.

(iii) 8 hours

(iv) 12 hours 15 minutes.

5. A clock gains 3 minutes every hour. If the clock is set correctly at 5 a.m. find the time shown by the clock at 7 p.m.?

Solution:

The clock set correctly at 5 am and it gain 3 minutes every hours.

Then, from 5 a.m. to 7 p.m. the time difference is 14 hours but we have to add 14*3=42 minutes as it gains every hours.

So, the time shown by the clock at 7 p.m. is 7:40 pm

6. If 11th of January 2018 is Thursday, what is the day on 20th July of the same year?

Solution:

The days between 11^th Jan to 20^th July is 191 days.

Then, the day is Saturday.

Summary

(I) Basic metric units of length is metre, weight is gram and capacity (volume) is litre.

(II) Different unit measurements should be converted into same unit for addition and subtraction of units.

(III) a.m. (antemeridian) denotes the time that is after 12:00 midnight and before 12:00 noon.

p.m. (postmeridian) denotes the time that is after 12:00 noon and before 12:00 midnight.

(IV) To convert 12 hour time to 24 hour time, add 12 to any hours 1 p.m. to 11 p.m. and change 12 a.m. as 00:00 hours.

(V) To convert given time greater than 12 in railway time to an ordinary time, subtract 12 from it. (VI) Ordinary and Railway time are the same in a.m. and it is less than 12.

(VII) In both the formats there is no change in minutes.

(VIII) A year which is divisible by 4 is considered as a leap year.

(XI) A century year which is divisible by 400 is a leap year.