basicmeasurements.docx

8/10/2019 BASICMEASUREMENTS.docx

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BASIC MEASUREMENTS

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LENGTH

A) Determining the Metric Units of Length


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1. Lenght is the distance between two points.

2. The relationships between the metric units

of legth are shown below :

Worked Example 1

State the units of length suitable for measuring

(a) the thickness of a coin,

(b) the length of Sungai Pahang.

Solution

(a) mm (b) km

B) Conversion between Metric Units of length

A unit of length can be converted to another

unit.

(a) 1 cm = 10 mm

(b) 1 m = 100 cm

(c) 1 m = 100 x 10 mm

= 1 000 m

(d) 1 km = 1 000 m

(e) 1 km = 1 000 x 100 cm

= 100 000 cm

(f) 1 km = 100 000 x 10 mm


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Worked Example 4

Convert

(a) 85 mm to cm and mm,

(b) 6 054

Solution

Worked Example 5

Convert

(a) 73 m to m and cm,4

(b) 0. 52 km to cm.

Solution


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curve MN.

MN= 4.6 cm or 4 cm 6 mm

D) Drawing Straight Lines

Use A straight line can be drawn by using a

ruler and a pencil if the length is given.

Worked Example 8

Draw the straight line PR with the length of

(a) 41 cm (b) 6 cm 4 mm.2

Solution

E) Estimating the Lengths of Objects

When estimating the length of an object,

an appropriate unit of length must be used.

For example :-

The appropriate unit of measurement for estimating

the thickness of a coin is mm. Other units of length

such as m and km are not suitable in this case. m

and km are used for larger measurement.


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Worked Example 9

Estimate the length of the fluorescent tube in metres.

Solution

The estimated length of the fluorescent tube is 1. 5 m.

The actual length is 1. 22 m.

F) Addition, Subtraction, Multiplicationand Division involving Length

Estimate Before performing addition, subtraction,

multiplication or division involving lengths of different

units, we have to change all the measurements to the

same unit first.

Worked Example 10

Solve

(a) 15 m 42 cm + 6 m 25 cm

(b) 24. 9 cm + 4 mm.

Solution

Therefore, 15 m 42 cm + 6 m 25 cm

= 21 m 67 cm


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Worked Example 11

Solve

(a) 6 cm - 2. 015 cm,

(b) 51 mm - 23 mm,2 10

(c) 33. 52 m - 16 cm.

Solution

(a) 6. 000 cm- 2. 015 cm

3. 985 cm

Therefore, 6 cm - 2. 015 cm = 3. 985 cm


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Worked Example 12

Solve

(a) 64 mm x 88

(b) 4 km 20 m 12 cm x 5

Solution

(a) 64 mm x 8

8

= 52 mm x 88

= 52 mm


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Therefore, 4 km 20 m 12 cm x 5

= 20 km 100 m 60 cm

Worked Example 13

Solve

(a) 18. 2 cm 5 (b) 15 km 280 4.

Solution

G) Problem Solving involing Length

Worked Example 14

A piece of black thread is 2 m 64 cm long and


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a piece of red thread is 2. 4 m long. Find their

total length.

Solution

1. Understand the problem

Length of the black thread = 2 m 64 cm

Length of red thread is 4. 6 m

Find : Total length of the two pieces of threads

2. Devise a plan

Change 2 m 64 cm to m and then nuse addition.

3. Carry out the plan

2 m 64 cm

= 2 m + ( 64 100) m

= 2 m + 0. 64 m

= 2. 64 m

2. 64 m + 2. 4 m = 5. 04m

2. 64 m+ 2. 40 m

5. 04 m

Therefore, the total length is 5. 04 m.

4. Check

5. 04 m- 2. 4 m

2. 64 m

MASS

A) Determining the Metric Units of Mass


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1. Mass is the amount of matter in an object.

2. Mass is usually measured in grams (g),

kilograms (kg) and tonnes in metric units.

3. A suitable unit of measured should be used

for determining the mass of an object.

Worked Example 15

State suitable unit for each of the following.

(a) The mass of a chicken

(b) The mass of an egg

Solution

(a) kg

(b) g

B) Conversion between Metric Units of Mass

The relationships between the units of

mass in the metric system are as follows.

Worked Example 16

Convert


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(a) 2. 45 kg to g,

(b) 3 106 kg to tonnes,

(c) 15 030 g to kg and g,

(d) 67. 05

Solution

C) Measuring the Mass of Objects

1. A weighing machine is used to measure


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the mass of an object.

2. Before weighing the object, the pointer

(needle) must be set at zero.

Worked Example 17

State the mass of each object on the weighing

machine below.

(a) (b)

Solution

(a) 300 g (b) 1. 8 kg

D) Estimating the Mass of Object

When estimating the mass of an object, an

appopriate unit of mass must be used.

For Example :-

The unit suitable for measuring the mass of

a 20 sen coin is g. kg is not suitable in this

case as kg is used for larger measurements.

Worked Example 18

Estimate the mass of

(a) a bottle of 300 ml of mineral water,

(b) a ream of A4 papers.


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Worked Example 20

Solve

(a) 5 tonnes 410 kg x 6

(b) 22 kg 45

(c) 20 kg 25 g 8

Solution


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F) Problem Solving involving Mass

An empty vessel weights 530 g. When filled

with sugar, it weights 2. 58 kg. Find, in kg,

the mass of the sugar.

Solution


Given information :

Mass of the empty vessel = 530 g

Mass of the empty vessel + sugar = 2. 58 kg


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Find : Mass of sugar

2. Devise a plan

Change the mass of the empty vessel to kg

and then use subtraction.


530 g

= ( 530 1 000 ) kg

0. 53 kg 2. 5 8 kg- 0. 5 3 kg

Mass of sugar 2. 0 5 kg

= 2. 58 kg - 0. 53 kg

= 2. 05 kg

Therefore, the mass of the sugar is 2. 05 kg.

4. Check

2. 05 kg

+ 0. 53 kg2. 58 kg

TIME

A) Determining the Appropriate Units of Time

1. Time is the period between two occurrences

or events.

2. The units of time are seconds, minutes, hours,

days, weeks, months, years, decades, centuries

and millenniums.

Worked Example 22


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State a suitable unit of time for each of the following.

(a) The age of a person

(b) The time taken to travel from Shah Alam to Kuala

Pilah by car

Solution

(a) Years and months

(b) Hours and minutes

B) Conversion between Units of Time

State a The relationships between the units of time

are as follows :

Worked Example 23

Convert

(a) 51 days to hours,4

(b) 6 minute 18 seconds to seconds.


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Solution

(a) 51 days = 21 x 24 hours4 4

= 126 hours

(b) 6 minute 12 seconds

= ( 6 x 60 ) seconds + 18 seconds

= ( 360 + 18 ) seconds

= 378 seconds

Worked Example 24

Convert

(a) 36 months to years,

(b) 309 minutes to hours and minutes.

Solution

(a) 32 months = ( 36 12 ) years

= 3 years

C) Measuring the Time taken for an Activity

A stop watch or a digital clock are always used to

measure he time taken for an activity. The units


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used are usually in seconds, minutes and hours.

D) Estimating the Time of an Activity

Estimate the time taken to sing the national anthem,

"Negaraku".

Solution

30 seconds

E) Addition, Subtraction, Multiplicationand Division involving Time

Worked Example 26

Solve

(a) 5 minutes 42 seconds + 31 minutes.2

Solution

(a) 5 minutes 42 seconds + 31 minutes2

= 5 minutes 42 seconds + 3 mminutes

30 seconds

= 9 minutes 12 seconds

Worked Example 27

Solve


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(a) 14 weeks 2 days - 6 weeks 5 days

(b) 22. 3 minutes - 24 seconds

Solution

(b) 22. 3 minutes - 24 seconds

= ( 22 + 0. 3) minutes - 24 seconds

= 22 minutes + ( 0. 3 * 60 ) seconds -

24 seconds

= 22 minutes 18 seconds - 24 seconds

= 21 minutes 54 seconds

Worked Example 28

Solve

(a) 8 days 15 hours x 4

Solution


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Worked Example 29

Solve

(a) 7 hours 12

Solution

(a) 7 hours 12

= ( 7 x 60 ) minutes 12

= 420 minutes 12

= 35 minutes

F) Problem Solving involving Time

Worked Example 30

A bus took 6 hours 35 minutes to travel from

Seremban to Ipoh. It took another 2 hours 15

minutes to travel from Ipoh to Butterworth.

Calculate the total time taken to travel from

Seremban to Butterworth.


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Solution


Given information :

Seremban to Ipoh = 6 hours 35 minutes

Ipoh to Butterworth = 2 hours 15 minutes

Find : Total time from Shah Alam to

Butterworth

2. Devise a plan

Use addition.


4. Check

8.4 TWELVE-HOUR AND TWENTY-FOUR-HOUR SYSTEM

A) Time in the 12-hour System

1. Time can be expressed in the 12-hour system

or 24-hour system.

2. In the 12-hour system, we have to state clearly

whether the time is in the morning, noon, after-


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noon, evening, night or midnight.

3. In the 12-hour system, a.m. is used for the time

between midnight and noon whereas p.m. is used

for the time between noon and midnight.

Solution

For example :-

Worked Example 31

Write the time for each of the following in the 12-

hour system.

(a) (b)

Solution

(a) 8. 20 a.m. (b) 3. 35 p.m.

B) Time in the 24-hour System

1. In the 24-hour system, four digits are used to

indicate time. The first two digits denote hour

and the last two digits dennite minutes.

For example :-


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2. A day ends at 2400 hours. The next day begins

at 0000 which is 12. 00 midnight.

Worked Example 32

Write the time for each of the following in the 24-

hour system.

(a) (b)

Solution

(a) 0805 hours (b) 1120 hours

C) Changing Time in the 12-hour Systemto the 24-hour System and vice versa

The relationship between the times in two systems

is shown below.


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Worked Example 33

Change each of the following to the 24-hour

system.

(a) 8. 15 a.m. (d) 10 .45 p.m.

(b) 11. 00 a.m. (e) 12. 20 a.m.

(c) 4. 35 p.m.

Solution

Worked Example 34

Change each of the following to the 12-hour

system.

(a) 0925 hours (c) 1705 hours


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(b) 1235 hours (d) 0045 hours

Solution

D) Determining the Interval betweenTwo given Times

Interval is the length of time between two given

times.

Worked Example 35

Find the interval between 09.15 a.m. and 3. 45 p.m.

on the same day.

Solution

Interval

= 2 hours 45 minutes + 3 hours 45 minutes

= 6 hours 30minutes

Worked Example 36

Find the interval between 11. 30 p.m. on Tuesday


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and 4. 15 a.m. on Wednesday.

Solution

Interval

= 30 minutes + 4 hours 15 minutes

= 4 hours 45 minutes

E) Determining the Time in the 12-hourSystem or 24-hour System

Worked Example 37

Find the time which is 5 hours 25 minutes after

2. 15 p.m., in the 12-hour system.

Solution

The time is 7. 40 p.m..

Worked Example 38

Find the time which is 5 hours 55 minutes before

2. 10 p.m., in the 12-hour System.


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2. Devise a plan

Change the times to the 24-hour system and

then use subtraction.


8. 45 a.m. = 0845 hours

3. 20 p.m. = 1520 hours

Therefore, the show lasts 6 hours 35 minutes.

4. Check


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