Mathematics Form 1 Chap 8

BASIC MEASUREMENTS  

                        -              

LENGTH

A) Determining the Metric Units of Length

1. Length is the distance between two points.

2. The relationships between the metric units of length are shown below :

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 measure 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.

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.

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

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. 

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) Estimating the Mass of Object

When estimating the mass of an object, an

appropriate unit of mass must be used.

For Example :-

The unit suitable for measuring the mass of a 20 cent coin is g. kg is not suitable in this  case as kg is used for larger measurements.

E) Addition, Subtraction, Multiplication and Division involving Mass

Before performing addition, subtraction, multiplication 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

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.

B) Conversion between Units of Time

State a The relationships between the units of time

are as follows :

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) Addition, Subtraction, Multiplication   and Division involving Time

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

Given information :

    Seremban to Ipoh = 6 hours 35 minutes Ipoh to Butterworth = 2 hours 15 minutesFind : Total time from Seremban to Butterworth 

6 hours 35 minutes+ 2 hours 15 minutes_____________________ 8 hours 50 minutes______________________

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- 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.

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 denote minutes.           

For example :-

2. A day ends at 2400 hours. The next day begins at 0000 which is 12. 00 midnight.

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

D) Determining the Interval between   Two 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 and 4. 15 a.m. on Wednesday.

Solution

Interval

= 30 minutes + 4 hours 15 minutes 

= 4 hours 45 minutes

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