
BASIC MEASUREMENTS 
LENGTH A) Determining the Metric Units of Length1. 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. 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 8.4 TWELVEHOUR AND TWENTY FOURHOUR SYSTEM A) Time in the 12hour System 1. Time can be expressed in the 12hour system or 24hour system. 2. In the 12hour system, we have to state clearly whether the time is in the morning, noon, after noon, evening, night or midnight. 3. In the 12hour 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 24hour System 1. In the 24hour 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 12hour System to the 24hour 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 24hour 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 12hour 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 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 E) Determining the Time in the 12hour System or 24hour System Worked Example 37 Find the time which is 5 hours 25 minutes after 2. 15 p.m., in the 12hour 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 12hour 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 12hour 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 24hour 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 

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