BASIC MEASUREMENTS
In this topic we will cover on several subtopics which are:
-
LENGTH
A) Determining the Metric Units of Length
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
= 1 000 000 mm
Worked Example 2
Convert
(a) 31 m to cm,
4
(b) 26 cm 2 mm to mm
Solution:
Worked Example 3
Convert
(a) 62.3 cm to m,
(b) 1 km 25 m to km.
Solution:
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:
C) Measuring the Lengths of Objects
Worked Example 6
Measure the length of the straight line PR with
a ruler.
Solution:
PR = 2.8 cm or 2 cm 8 mm
Worked Example 7
Mesure the curve MN.
Solution:
Use a piece of thread and place it on the curve
from M to N. Mark the point N on it. Stretch the
thread on a ruler to mesure the length of the
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.
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, Multiplication and 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
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
Worked Example 12
Solve
(a) 64 mm x 8
8
(b) 4 km 20 m 12 cm x 5
Solution:
(a) 64 mm x 8
8
= 52 mm x 8
8
= 52 mm
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
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
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
(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
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.
Solution:
(a) Using a packet of 300 g of sugar as a guide,
the estimated mass of the bottle of mineral
water is about 300 g. The actual mass of the
bottle of mineral water is 310 g.
(b) Using a packet of flour weighing 1 kg as a
guide, the mass of a ream of A4 paper is
estimated to be about 2 kg. The actual mass
of a ream of A4 paper is 2. 38 kg.
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.
Solution:
(a) Using a packet of 300 g of sugar as a guide,
the estimated mass of the bottle of mineral
water is about 300 g. The actual mass of the
bottle of mineral water is 310 g.
(b) Using a packet of flour weighing 1 kg as a
guide, the mass of a ream of A4 paper is
estimated to be about 2 kg. The actual mass
of a ream of A4 paper is 2. 38 kg.
E) Addition, Subtraction, Multiplication and Division involving Mass
Before performing addition, subtraction,multip-
lication and division involving mass, change all
the measurements to the same unit.
Worked Example 19
Solve
(a) 8 tonnes 350 kg + 6 tonnes 740 kg,
(b) 13 kg 70 g - 4 kg 520 g
(c) 720 g - 3 kg
5
Solution:
Worked Example 20
Solve
(a) 5 tonnes 410 kg x 6
(b) 22 kg ÷ 4
5
(c) 20 kg 25 g ÷ 8
Solution
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:
1. Understand the problem
Given information :
Mass of the empty vessel = 530 g
Mass of the empty vessel + sugar = 2. 58 kg
Find : Mass of sugar
2. Devise a plan
Change the mass of the empty vessel to kg
and then use subtraction.
3. Carry out the plan
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 kg
2. 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
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.
Solution:
(a) 51 days = 21 x 24 hours
4 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
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, Multiplication and Division involving Time
Worked Example 26
Solve
(a) 5 minutes 42 seconds + 31 minutes.
2
Solution:
(a) 5 minutes 42 seconds + 31 minutes
2
= 5 minutes 42 seconds + 3 mminutes
30 seconds
= 9 minutes 12 seconds
Worked Example 27
Solve
(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:
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.
Solution:
1. Understand the problem
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.
3. Carry out the plan
4. Check
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-
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 :-
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 System to the 24-hour System and vice versa
The relationship between the times in two systems
is shown below.
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
(b) 1235 hours (d) 0045 hours
Solution:
D) Determining the Interval between two given times
- Interval is the length of time between two give 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
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-hour System 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.
Solution:
2. 10 p.m. = 1410 hours
The time is 8. 15 a.m..
Worked Example 39
Find the time which is 4 hours 50 minutes after
2120 hours, in the 12-hour system.
Solution:
The time is 0210 hours, the next day.
F) Problem Solving involving Time
A show starts at 8. 45 a.m. and ends at 3. 20 p.m.
How long is the show?
Solution:
1. Understand the problem
Given information :
The show starts at 8. 45 a.m..
The show ends st 3. 20 p.m..
Find : Duration of the show
2. Devise a plan
Change the times to the 24-hour system and
then use subtraction.
3. Carry out the plan
8. 45 a.m. = 0845 hours
3. 20 p.m. = 1520 hours
Therefore, the show lasts 6 hours 35 minutes.
4. Check
GLOSSARY
- BASIC MEASUREMENT- ukuran asas
- LENGHT- panjang
- THICKNESS- ketebalan
- DISTANCE- jarak
- STRAIGHT LINE- garis lurus
- MASS- jisim
- TIME- masa
- SECOND- saat
- MINUTE- minit
- HOUR- jam
- WEEK- minggu
- MONTH- bulan
- YEAR- tahun
- DECADE- dekad
- CENTURY- abad
- MILLENIUM- milenium
- INTERVAL- tempoh masa
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Fikir2kan lah & Selamat Berjuang ("-")v
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