Steady Matematik Tingkatan 3

PELAPNELGAINBGESITBSEESLTLSERLLER TINGKATAN

STEADY! 3

MATEMATIK KSSM

Mathematics

BONUS ›› Mesra buku teksBUKU
›› Ingatan & tip segera
Langkah ›› Contoh penyelesaian & latih tubi
Penyelesaian ›› KBAT & i-THINK
Lengkap untuk ›› Praktis subtopik berformat PT3
SEMUA Soalan
disediakan dalam B

Kod QR

K. W. Chiang

EDISI GURU

KKAaNnDdUuNnGgAaNn

Rekod Pencapaian Pentaksiran Murid 6BAB Sudut dan Tangen bagi Bulatan 24
Angles and Tangents of Circles

2BAB Bentuk Piawai 1 6.1 Sudut pada Lilitan dan Sudut Pusat yang 24
Standard Form Dicangkum oleh Suatu Lengkok 30
35
2.1 Angka Bererti 1 Praktis Berformat PT3 44
Praktis Berformat PT3 6.2 Sisi Empat Kitaran
Praktis Berformat PT3 49
2.2 Bentuk Piawai 4 6.3 Tangen kepada Bulatan
Praktis Berformat PT3 Praktis Berformat PT3
6.4 Sudut dan Tangen bagi Bulatan
Praktis Berformat PT3

8BAB Lokus dalam Dua Dimensi
Loci in Two Dimensions

8.1 Lokus 49
Praktis Berformat PT3

4BAB Lukisan Berskala 11 8.2 Lokus dalam Dua Dimensi 53
Scale Drawings Praktis Berformat PT3

4.1 Lukisan Berskala 11 Jawapan J1-J8
Praktis Berformat PT3

Langkah Penyelesaian Lengkap Kod QR

2BAB Bentuk Piawai
Standard Form

2.1 Angka Bererti BUKU TEKS ms. 32 – 36

Significant Figures (d) Semua digit sifar di bahagian akhir suatu nombor
bulat bukan angka bererti kecuali dinyatakan.
MESTI TAHU & INGAT All zeros at the end of a whole number are not significant
figures unless stated otherwise.
1. Angka bererti merujuk kepada semua nombor digit
yang relevan dalam suatu integer atau perpuluhan Contohnya / For example:
yang dibundarkan kepada suatu darjah ketepatan. 199 = 200
Significant figures refer to all relevant digits in an integer or (1 angka bererti jika tahap kejituan ialah ratus
a decimal rounded to a certain degree of accuracy.
terhampir)
2. Bagi suatu nombor lebih besar daripada 1, (1 significant figure if the level of accuracy is to the
For a number that is greater than 1,
nearest hundred)
(a) Semua sifar antara digit bukan sifar ialah angka 999 = 1 000
bererti. (2 angka bererti jika tahap kejituan ialah ratus
All zeros between non-zero digits are significant figures.
terhampir)
Contohnya / For example: (2 significant figures if the level of accuracy is to the
3 009 (4 angka bererti / significant figures)
607.08 (5 angka bererti / significant figures) nearest hundred)

(b) Semua digit bukan sifar ialah angka bererti. 3. Bagi suatu nombor yang kurang daripada 1, semua
All non-zero digits are significant figures. digit sifar sebelum digit bukan sifar dalam perpuluhan
bukan angka bererti.
Contohnya / For example: For a number that is less than 1, all zeros before the non-zero
2 137 (4 angka bererti / significant figures) digit in a decimal are not significant figures.
359 (3 angka bererti / significant figures)
Contohnya / For example:
(c) Semua digit sifar di bahagian akhir suatu 0.06 (1 angka bererti / significant figure)
perpuluhan ialah angka bererti. 0.0098 (2 angka bererti / significant figures)

All zeros at the end of a decimal are significant figures.
Contohnya / For example:
3.50 (3 angka bererti / significant figures)
8.200 (4 angka bererti / significant figures)

A Nyatakan bilangan angka bererti bagi nombor-nombor yang berikut. TP 1 ARAS R
State the number of significant figures for the following numbers.

Contoh 1. 3 022 2. 409
4 a.b. /s.f. 3 a.b. /s.f.
4 035
  4 a.b. /s.f.

Contoh 3. 3.456 4. 0.0023
4 a.b. /s.f. 2 a.b. /s.f.
8.061
  4 a.b. /s.f.

1 © Penerbitan Pelangi Sdn. Bhd.

  Matematik  Tingkatan 3 Bab 2 Bentuk Piawai

B Lengkapkan jadual berikut dengan membundarkan setiap nombor betul kepada angka bererti yang diberi.

Complete the following table by rounding off each number correct to the given significant figures. TP 2 ARAS R

Nombor / Number 1 Angka bererti / Significant figures 3
2
Contoh 400 389
389 390
600 568
1. 568 200 570 245
2. 245 3 000 250 2 980
3. 2 976 5 3 000 4.87
4. 4.87 2 4.9 1.69
5. 1.692 6 1.7 5.60
6. 5.601 0.5 5.6 0.468
7. 0.4676 0.07 0.47 0.0684
8. 0.06839 0.005 0.068 0.00502
9. 0.005018 0.0050

C Hitung setiap yang berikut. Nyatakan jawapan betul kepada angka bererti yang dinyatakan dalam kurungan.

Calculate each of the following. State the answer correct to the significant figures shown in the brackets. TP 3 ARAS R

Contoh 1. 4.79 × 6.9 – 0.82   [4]
= 33.051 – 0.82
2.59 × 4.8 + 0.67   [3] = 32.231
= 12.432 + 0.67 = 32.23 (4 a.b. / s.f.)
= 13.102
= 13.1 (3 a.b. / s.f.)

2. 8.53 ÷ 0.2 + 3.48   [2] 3. 36.46 – 4.5 × 3.8  [3]
= 42.65 + 3.48 = 36.46 – 17.1
= 46.13 = 19.36
= 46 (2 a.b. / s.f.) = 19.4 (3 a.b. / s.f.)

4. 47.42 + 41.3 ÷ 2.5 [2] 5. 7.41 × 0.5 ÷ 0.3 + 8.6 [3]
= 47.42 + 16.52 = 3.705 ÷ 0.3 + 8.6
= 63.94 = 12.35 + 8.6
= 64 (2 a.b. / s.f.) = 20.95
= 21.0 (3 a.b. / s.f.)

6. 30.45 ÷ 0.3 – 5.2 × 0.4  [1] 7. 38.27 – 3.53 × 0.4 + 8.5   [4]
= 101.5 – 2.08 = 38.27 – 1.412 + 8.5
= 99.42 = 36.858 + 8.5
= 100 (1 a.b. / s.f.) = 45.358
= 45.36 (4 a.b. / s.f.)

© Penerbitan Pelangi Sdn. Bhd. 2

Matematik  Tingkatan 3 Bab 2 Bentuk Piawai 

Praktis BerfKoArNmDaUtNGPATN3

1. Bundarkan 234 694 betul kepada empat angka bererti. 6. (a) Bundarkan setiap nombor yang berikut kepada
Round off 234 694 correct to four significant figures.
A 234 000 bilangan angka bererti yang dinyatakan.
B 234 600 Round off each of the following numbers to the number
C 234 700
D 235 000 of significant figures as stated. i-THINK

2. Antara nombor berikut, yang manakah mempunyai [4 markah / 4 marks]
tiga angka bererti?
Which of the following numbers has three significant figures? Jawapan / Answer:
A 2 543
B 2 025 0.00368 1 a.b. / 1 s.f. 0.004
C 0.240 0.293 0.3
D 0.008 0.0000478 Dibundarkan 1 a.b. / 1 s.f. 0.000048
0.05974 0.060
3. Berapakah bilangan angka bererti bagi nombor kepada 2 a.b. / 2 s.f.
672 000? Rounded off to 2 a.b. / 2 s.f.
How many significant figures are there in 672 000?
A 3 (b) Tentukan bilangan angka bererti bagi setiap nombor
B 4
C 5 yang berikut.
D 6 Determine the number of significant figures of the

4. 685 674 menjadi 686 000 selepas dibundarkan kepada following numbers. [4 markah / 4 marks]
685 674 becomes 686 000 after rounded off to
A 2 angka bererti / significant figures Jawapan / Answer:
B 3 angka bererti / significant figures
C 4 angka bererti / significant figures (i) 4.08 : 3 a.b./s.f.
D 5 angka bererti / significant figures
(ii) 9.00007 : 6 a.b./s.f.
5. Padankan dengan betul apabila nombor berikut
dibundarkan kepada tiga angka bererti. (iii) 0.0006 : 1 a.b./s.f.
Match correctly when the following numbers are rounded off
to three significant figures. (iv) 2 500 : 2 a.b./s.f.
[4 markah / 4 marks]
(c) Cari nilai bagi 9.823 – 0.78 ÷ 5 dan bundarkan
Jawapan / Answer: jawapan anda betul kepada tiga angka bererti.

358 400 Find the value of 9.823 – 0.78 ÷ 5 and round off the
answer correct to three significant figures.
358 689 358 000
[2 markah / 2 marks]

Jawapan / Answer:
9.823 – 0.78 ÷ 5
= 9.823 – 0.156
= 9.667
= 9.67 (3 a.b. / s.f.)

358 240 359 000

358 764

3 © Penerbitan Pelangi Sdn. Bhd.

  Matematik  Tingkatan 3 Bab 2 Bentuk Piawai

2.2 Bentuk Piawai BUKU TEKS ms. 37 – 44

Standard Form

MESTI TAHU & INGAT

1. Bentuk piawai ialah suatu cara menulis nombor tunggal dalam bentuk A × 10n dengan keadaan 1  A  10 dan n ialah
integer.
The standard form is a way to write a single number in the form A × 10n , where 1  A  10 and n is an integer.

2. Nilai ukuran sistem metrik dalam bentuk piawai ditunjukkan dalam jadual di bawah.
The value of measurements in the metric system in standard form is shown in the table below.

Awalan Simbol Bentuk piawai Nombor tunggal
Prefix Symbol Standard form Single number

eksa / exa E 1 × 1018 1 000 000 000 000 000 000
peta P 1 × 1015 1 000 000 000 000 000
tera T 1 × 1012 1 000 000 000 000
giga G 1 × 109 1 000 000 000
mega M 1 × 106 1 000 000
kilo k 1 × 103 1 000
h 1 × 102 100
hekto / hecto da 1 × 101 10
deka d 1 × 10–1 0.1
c 1 × 10–2 0.01
desi / deci m 1 × 10–3 0.001
senti / centi µ 1 × 10–6 0.000 001
mili / milli n 1 × 10–9 0.000 000 001
mikro / micro p 1 × 10–12 0.000 000 000 001
f 1 × 10–15 0.000 000 000 000 001
nano a 1 × 10–18
piko / pico 0.000 000 000 000 000 001

femto
atto

3. Peraturan yang melibatkan operasi +, –, × dan ÷ untuk nombor dalam bentuk piawai adalah seperti berikut.
The rules involving operations of +, –, × and ÷ on numbers in standard form are as follows.
(a) a × 10m + b × 10m = (a + b) × 10m (b) a × 10m – b × 10m = (a – b) × 10m
(c) a × 10m × b × 10n = (a × b) × 10m + n (d) a × 10m ÷ b × 10n = (a ÷ b) × 10m – n

D Tuliskan setiap nombor yang berikut dalam bentuk piawai. TP 2 ARAS R
Write each of the following numbers in standard form.

Contoh 1. 12 = 1.2 × 101 2. 2 650 = 2.65 × 103
356 = 3.56 × 102

Contoh 3. 285 000 = 2.85 × 105 4. 9 200 000 = 9.2 × 106
430 000 = 4.3 × 105

Contoh 5. 8 220.7 = 8.2207 × 103 6. 181.2 = 1.812 × 102
423.7 = 4.237 × 102

© Penerbitan Pelangi Sdn. Bhd. 4

Contoh 7. 0.0854 = 8.54 × 10–2 Matematik  Tingkatan 3 Bab 2 Bentuk Piawai 
0.091 = 9.1 × 10–2 9. 0.0000417 = 4.17 × 10–5
8. 0.00475 = 4.75 × 10–3
Contoh
0.00058 = 5.8 × 10–4 10. 0.00000327 = 3.27 × 10–6

E Nyatakan setiap yang berikut sebagai suatu nombor tunggal. TP 2 ARAS R
State each of the following as a single number.

Contoh 1. 5.6 × 10 2. 5.47 × 103
= 56 = 5 470
4.0 × 103
= 4 000

Contoh 3. 0.035 × 107 4. 0.088 × 103
= 350 000 = 88
0.85 × 105
= 85 000

Contoh 5. 7 × 10–3 6. 8 × 10–4
= 0.007 = 0.0008
6 × 10–2
= 0.06

Contoh 7. 2.6 × 10–4 8. 6.7 × 10–5
= 0.00026 = 0.000067
1.53 × 10–7
= 0.000000153

F Tukarkan ukuran dalam sistem metrik yang berikut kepada unit dalam kurungan. Nyatakan jawapan anda dalam bentuk
piawai. TP 2 ARAS R

Convert the following measurements in metric system to the units in the brackets. State your answer in standard form.

Contoh 1. 436 gigabait / gigabytes [bait / bytes]
3 050 kilometer / kilometres [meter / metres] = 4.36 × 10  2 × 109 bait / bytes
= 3.05 × 10  3 × 103 meter / metres = 4.36 × 10  2 + 9 bait / bytes
= 3.05 × 10  3 + 3 meter / metres
= 4.36 × 1011 bait / bytes

= 3.05 × 106 meter / metres

2. 0.83 teraliter / teralitres [liter / litres] 3. 98 mikrometer / micrometres [meter / metres]
= 8.3 × 10  –1 × 1012 liter / litres = 9.8 × 10  1 × 10–6 meter / metres
= 8.3 × 10  –1 + 12 liter / litres = 9.8 × 10  1 + (–6) meter / metres

= 8.3 × 1011 liter / litres = 9.8 × 10–5 meter / metres

5 © Penerbitan Pelangi Sdn. Bhd.

  Matematik  Tingkatan 3 Bab 2 Bentuk Piawai

G Hitung setiap yang berikut dan nyatakan jawapan anda dalam bentuk piawai. TP 3 ARAS R
Calculate each of the following and state your answer in standard form.

Contoh 1. 5.1 × 106 + 3.5 × 106 2. 6.3 × 103 + 1.3 × 103
3.4 × 104 + 3.6 × 104 = (5.1 + 3.5) × 106 = (6.3 + 1.3) × 103
= (3.4 + 3.6) × 104 = 8.6 × 106 = 7.6 × 103
= 7 × 104

Contoh 3. 4.56 × 103 – 2.32 × 103 4. 5.4 × 104 – 3.6 × 104
9.3 × 105 – 6.5 × 105 = (4.56 – 2.32) × 103 = (5.4 – 3.6) × 104
= (9.3 – 6.5) × 105 = 2.24 × 103 = 1.8 × 104
= 2.8 × 105

Contoh 5. 4 × 5 × 103 6. 7.2 × 5 × 104
3 × 8 × 102 = 20 × 103 = 36 × 104
= 24 × 102 = 2 × 101 × 103 = 3.6 × 101 × 104
= 2.4 × 101 × 102 = 2 × 101 + 3 = 3.6 × 101 + 4
= 2.4 × 101 + 2 = 2 × 104 = 3.6 × 105
= 2.4 × 103

Contoh 7. 1.6 × 105 8. 1.56 × 104
5 12
3.5 × 106
= 1.6 × 105 = 1.56 × 104
7 5 12
3.5
= 7 × 106 = 0.32 × 105 = 0.13 × 104

= 0.5 × 106 = 3.2 × 10–1 × 105 = 1.3 × 10–1 × 104
= 3.2 × 10-1 + 5 = 1.3 × 10-1 + 4
= 5 × 10–1 × 106
= 5 × 10–1 + 6 = 3.2 × 104 = 1.3 × 103

= 5 × 105

Contoh 9. 3.4 × 105 + 8.5 × 106 10. 9.4 × 103 + 3.8 × 104
2.4 × 102 + 3.5 × 103 = 3.4 × 105 + 8.5 × 10 × 105 = 9.4 × 103 + 3.8 × 10 × 103
= 2.4 × 102 + 3.5 × 101 × 102 = 3.4 × 105 + 85 × 105 = 9.4 × 103 + 38 × 103
= 2.4 × 102 + 35 × 102 = (3.4 + 85) × 105 = (9.4 + 38) × 103
= (2.4 + 35) × 102 = 88.4 × 105 = 47.4 × 103
= 37.4 × 102 = 8.84 × 101 × 105 = 4.74 × 101 × 103
= 3.74 × 101 × 102 = 8.84 × 106 = 4.74 × 104
= 3.74 × 103

Contoh 11. 4.8 × 103 – 5.1 × 102 12. 9.7 × 108 – 4.6 × 107
8.4 × 105 – 3.5 × 104 = 4.8 × 101 × 102 – 5.1 × 102 = 9.7 × 101 × 107 – 4.6 × 107
= 8.4 × 101 × 104 – 3.5 × 104 = 48 × 102 – 5.1 × 102 = 97 × 107 – 4.6 × 107
= 84 × 104 – 3.5 × 104 = (48 – 5.1) × 102 = (97 – 4.6) × 107
= (84 – 3.5) × 104 = 42.9 × 102 = 92.4 × 107
= 80.5 × 104 = 4.29 × 101 × 102 = 9.24 × 101 × 107
= 8.05 × 101 × 104 = 4.29 × 101 + 2 = 9.24 × 101 + 7
= 8.05 × 101 + 4 = 4.29 × 103 = 9.24 × 108
= 8.05 × 105

© Penerbitan Pelangi Sdn. Bhd. 6

Contoh 13. 8.3 × 106 × 4.6 × 107 Matematik  Tingkatan 3 Bab 2 Bentuk Piawai 
9 × 104 × 7.5 × 102 = 8.3 × 4.6 × 106 + 7
= 9 × 7.5 × 104 + 2 = 38.18 × 1013 14. 3.7 × 106 × 5.7 × 103
= 67.5 × 106 = 3.818 × 101 × 1013 = 3.7 × 5.7 × 106 + 3
= 6.75 × 101 × 106 = 3.818 × 101 + 13 = 21.09 × 109
= 6.75 × 101 + 6 = 3.818 × 1014 = 2.109 × 101 × 109
= 6.75 × 107 = 2.109 × 101 + 9
= 2.109 × 1010
Contoh
(2.4 × 105) ÷ (3 × 102) 15. (5.94 × 106) ÷ (6 × 103) 16. (3.4 × 107) ÷ (4 × 105)
= (2.4 ÷ 3) × 105 – 2 = (5.94 ÷ 6) × 106 – 3 = (3.4 ÷ 4) × 107 – 5
= 0.8 × 103 = 0.99 × 103 = 0.85 × 102
= 8 × 10–1 × 103 = 9.9 × 10–1 × 103 = 8.5 × 10–1 × 102
= 8 × 102 = 9.9 × 102 = 8.5 × 101

Contoh 17. 7.3 × 10–3 + 3.23 × 10–3 18. 8.76 × 10–5 + 2.65 × 10–5
2.47 × 10–4 + 8.35 × 10–4 = (7.3 + 3.23) × 10–3 = (8.76 + 2.65) × 10–5
= (2.47 + 8.35) × 10–4 = 10.53 × 10–3 = 11.41 × 10–5
= 10.82 × 10–4 = 1.053 × 101 × 10–3 = 1.141 × 101 × 10–5
= 1.082 × 101 × 10–4 = 1.053 × 10–2 = 1.141 × 10–4
= 1.082 × 10–3
19. 2.33 × 10–2 – 1.2 × 10–2 20. 9.76 × 10–3 – 1.5 × 10–3
Contoh = (2.33 – 1.2) × 10–2 = (9.76 – 1.5) × 10–3
8.3 × 10–4 – 6.2 × 10–4 = 1.13 × 10–2 = 8.26 × 10–3
= (8.3 – 6.2) × 10–4
= 2.1 × 10–4

Contoh 21. 5.6 × 2 × 102 22. 1.12 × 104
40 000 2.8 × 107
0.334 × 300 5.6 × 2 × 102
3 × 104 = 4 × 104 = 1.12 × 104 – 7
2.8
= 0.334 × 3 × 102 = 5.6 × 2 × 102 – 4 = 0.4 × 10–3
3 × 104 4
= 4 × 10–1 × 10–3
= 0.334 × 3 × 102 – 4 = 2.8 × 10–2 = 4 × 10–4
3
= 0.334 × 10–2
= 3.34 × 10–1 × 10–2
= 3.34 × 10–3

7 © Penerbitan Pelangi Sdn. Bhd.

  Matematik  Tingkatan 3 Bab 2 Bentuk Piawai

H Selesaikan setiap masalah yang berikut dan berikan jawapan anda dalam bentuk piawai, betul kepada tiga angka bererti,
jika perlu. TP 4 ARAS S

Solve each of the following problems and give your answer in standard form, correct to three significant figures, if necessary.

Contoh 1. Zul ingin memindahkan data berkapasiti 2 terabait ke
Sebuah bekas berukuran 60 cm × 36 cm × 35 cm. Hitung isi pemacu pen yang setiapnya berkapasiti 64 gigabait.
padu air yang boleh diisi penuh ke dalam bekas itu, dalam Hitung bilangan minimum pemacu pen berkapasiti 64
liter. gigabait yang diperlukan.
Zul wants to transfer 2 terabytes of data to pen drives with
A container measures 60 cm × 36 cm × 35 cm. Calculate the each of them with a capacity of 64 gigabytes. Calculate the
volume of water that can completely fill the container, in litres. minimum number of 64 gigabytes pen drives needed.

60 × 36 × 35 = 75 600 cm3 Bilangan minimum pemacu pen
= 75 600 ml Minimum number of pen drives
= 75 600 ÷ 1 000 l
= 75.6 l = 2 × 1012 bait  /  2 × 1012 bytes
= 7.56 × 10 l 64 × 109 bait 64 × 109 bytes

= 2 × 1012 – 9
64
= 0.03125 × 103

= 31.25
 32

2. Kelajuan cahaya ialah 3 × 108 m s–1. Hitung masa, 3. 2 255 keping jubin yang berukuran 30 cm × 30 cm
dalam saat, yang diambil oleh cahaya untuk bergerak diperlukan untuk dipasang pada lantai sebuah rumah
sejauh 200 km. Hitung luas lantai rumah, dalam meter persegi.
The speed of light is 3 × 108 m s–1. Calculate the time, in 2 255 pieces of tiles measuring 30 cm × 30 cm are required
seconds, taken by light to travel a distance of 200 km. to be laid on the floor of a house. Calculate the area of the
floor, in square metres.
   Masa =Jarak
Laju / Time = Distance Luas lantai / Area of the floor
Speed = 0.3 m × 0.3 m × 2 255
= 202.95 m2
Masa / Time = 3 200 km = 2.0295 × 102 m2
× 108 m s–1 = 2.03 × 102 m2 (3 a.b. / s.f.)
200 × 103 m
= 3 × 108 m s–1

= 66.7 × 103 – 8 s
= 6.67 × 101 × 10–5
= 6.67 × 10–4 s (3 a.b. / s.f.)



I Diberi g = 6.4 × 103 dan h = 4.32 × 104. Hitung nilai bagi operasi yang berikut. Nyatakan jawapan anda dalam bentuk
piawai dan betul kepada tiga angka bererti. TP 4 ARAS S

It is given that g = 6.4 × 103 and h = 4.32 × 104. Evaluate the following operations. State your answer in standard form and correct

to three significant figures.

Contoh 1. 2g
3gh 3h
= 3 × 6.4 × 103 × 4.32 × 104
= (3 × 6.4 × 4.32) × 103 × 104 = 2 × 6.4 × 103
= 82.944 × 103 + 4 3 × 4.32 × 104
= 8.2944 × 101 × 107 2 × 6.4
= 8.2944 × 108 = 3 × 4.32 × 103 – 4
= 8.29 × 108 (3 a.b. / s.f.)
= 0.9877 × 10–1
= 9.877 × 10–1 × 10–1
= 9.88 × 10–2 (3 a.b. / s.f.)

© Penerbitan Pelangi Sdn. Bhd. 8

Matematik  Tingkatan 3 Bab 2 Bentuk Piawai 

2. h–g 3. g–1 + h–1
gh
= (6.4 × 103)–1 + (4.32 × 104)–1

= 4.32 × 104 – 6.4 × 103 = (6.4 1 103) + 1 104)
6.4 × 103 × 4.32 × 104 × (4.32 ×

= 4.32 × 101 × 103 – 6.4 × 103 = 1 + 1
(6.4 × 4.32) × 103 × 104 6.4 × 103 4.32 × 10 × 103

= (43.2 – 6.4) × 103 = 1 × 10–3 + 1 × 10–3
(6.4 × 4.32) × 103 + 4 6.4 43.2

= 36.8 × 103   = 1 + 1 × 10–3
27.648 × 107 6.4 43.2

= 36.8 × 103 – 7 = 0.1794 × 10–3
27.648 = 1.794 × 10–1 × 10–3
= 1.794 × 10–4
= 1.331 × 10–4 = 1.79 × 10–4 (3 a.b. / s.f.)
= 1.33 × 10–4 (3 a.b. / s.f.)

Praktis BerfKoArNmDaUtNGPATN3

1. Ungkapkan 847 000 dalam bentuk piawai. 5. Lengkapkan operasi berikut.
Express 847 000 in standard form. PT3 Complete the following operations.

A 0.847 × 106 C 8.47 × 104 Jawapan / Answer : [4 markah / 4 marks]
(a) 4 × 105 × 6 × 105
B 8.47 × 105 D 8.47 × 10–5 = 24 × 1010

2. Ungkapkan 2.07 × 10–3 sebagai satu nombor tunggal. = 2.4 × 10  11
Express 2.07 × 10–3 as a single number.

A 0.000207 C 0.0207

B 0.00207 D 0.207 (b) 2 × 106
5 × 103
3. 0.0048 ditulis sebagai p × 10q dalam bentuk piawai.
= 0.4 × 103
Cari nilai p dan nilai q.
0.0048 is written as p × 10q in the standard form. Find the = 4 × 10  2
value of p and of q.

A p = 4.8, q = –3 C p = 48, q = –4 6. (a) Lengkapkan langkah-langkah pengiraan yang
berikut.
B p = 4.8, q = 3 D p = 48, q = 4
Complete the following steps in the calculation below.
4. Susun nombor berikut mengikut tertib menaik. [4 markah / 4 marks]
Arrange the following numbers in ascending order.
Jawapan / Answer :
6.0 × 10–5 9.0 × 10–3 3.5 × 10–5 1.05 × 10–5 6.8 × 10–6 + 3.5 × 10–5
[4 markah / 4 marks]
= 6.8 × 10  –1 × 10–5 + 3.5 × 10–5
Jawapan / Answer :
1.05 × 10–5, 3.5 × 10–5, 6.0 × 10–5, 9.0 × 10–3 = 0.68 × 10–5 + 3.5 × 10–5

= (0.68 + 3.5) × 10–5

= 4.18 × 10–5

9 © Penerbitan Pelangi Sdn. Bhd.

  Matematik  Tingkatan 3 Bab 2 Bentuk Piawai Jawapan / Answer :
Bilangan saat dalam satu tahun
(b) Selesaikan 7.49 × 10–7 – 2.6 × 10–8. Nyatakan Number of seconds in a year
jawapan anda dalam bentuk piawai. = 365 × 24 × 60 × 60
= 3.1536 × 107 s
Solve 7.49 × 10–7 – 2.6 × 10–8. State your answer in
standard form. Satu tahun cahaya
[3 markah / 3 marks] One light year
= 300 000 × 3.1536 × 107
Jawapan / Answer : = 9.4608 × 1012 km
7.49 × 10–7 – 2.6 × 10–8 = 9.4608 × 1012 × 105 cm
= 7.49 × 10–7 – 2.6 × 10–1 × 10–7 = 9.4608 × 1017 cm
= 7.49 × 10–7 – 0.26 × 10–7
= (7.48 – 0.26) × 10–7
= 7.22 × 10–7

(c) Laju cahaya ialah 300 000 km s–1. Hitung, satu
tahun cahaya, dalam cm, iaitu jarak yang dilalui
cahaya dalam satu tahun.

The speed of light is 300 000 km s–1. Calculate one light
year, in cm, which is the distance travelled by light in
one year.

[Anggap 1 tahun = 365 hari]
[Assume 1 year = 365 days]

[3 markah / 3 marks]

Mahir KKABNADTUN! GAN

1. Ketebalan sehelai kertas ialah 6 × 10–3 mm. Tinggi sejumlah kertas yang sama ialah 58.4 cm. Hitung bilangan helaian
kertas itu dan ungkapkan jawapan dalam bentuk piawai betul kepada satu angka bererti.
The thickness of a sheet of paper is 6 × 10–3 mm. The height of a stack of paper is 58.4 cm. Calculate the number of sheets of
paper and express the answer in standard form correct to one significant figure.

Bilangan helaian kertas
Number of sheets of paper

= 58.4 cm
6 × 10–3 mm

= 58.4 × 10 mm
6 × 10–3 mm

= 5.84 × 102
6 × 10–3

= 5.84 × 102 – (–3)
6
= 0.973 × 105
= 9.73 × 10–1 × 105
= 9.73 × 10–1 + 5
= 9.73 × 104
= 10 × 104
= 1 × 105 (1 a.b. / s.f.)

© Penerbitan Pelangi Sdn. Bhd. 10

KJAANWDUANPGAANN

2BAB Bentuk Piawai (b) (i) 3
Standard Form (ii) 6
(iii) 1
(iv) 2

(c) 9.67

A 1. 4 D 1. 1.2 × 101

2. 3 2. 2.65 × 103
3. 4 3. 2.85 × 105
4. 2 4. 9.2 × 106
5. 8.2207 × 103
B 1. 600 570 568 6. 1.812 × 102
7. 8.54 × 10–2
2. 200 250 245 8. 4.75 × 10–3
3. 3 000 3 000 2 980 9. 4.17 × 10–5
4. 4.87 10. 3.27 × 10–6
5. 5 4.9 1.69
6. 2 1.7 5.60 E 1. 56
7. 6 5.6 0.468
8. 0.5 0.47 0.0684 2. 5 470
9. 0.07 0.068 0.00502
0.005 0.0050 3. 350 000

C 1. 32.23 4. 88

2. 46 5. 0.007
3. 19.4
4. 64 6. 0.0008
5. 21.0
6. 100 7. 0.00026
7. 45.36
8. 0.000067

F 1. 436 gigabait / gigabytes [bait / bytes]

= 4.36 × 10  2 × 109 bait / bytes

Praktis BerfKoArNmDaUtNGPATN3 × 10  2 + 9 bait / bytes

1. C = 4.36

2. C = 4.36 × 1011 bait / bytes

3. A 2. 0.83 teraliter / teralitres [liter / litres]

4. B

5. = 8.3 × 10  –1 × 1012 liter / litres

358 400

358 689 358 000 = 8.3 –1 + 12 liter / litres

× 10 

= 8.3 × 1011 liter / litres

358 240 359 000 3. 98 mikrometer / micrometres [meter / metres]

358 764 = 9.8 1 10–6 meter / metres

× 10  ×

6. (a)  0.00368 1 a.b. / 1 s.f. 0.004 = 9.8 1 + (–6) meter / metres
0.293
0.0000478 × 10 
0.05974
Dibundarkan 1 a.b. / 1 s.f. 0.3 = 9.8 × 10–5 meter / metres

kepada 2 a.b. / 2 s.f. G 1. 8.6 × 106
Rounded 2 a.b. / 2 s.f. 0.000048
2. 7.6 × 103
off to 0.060 3. 2.24 × 103

J1 © Penerbitan Pelangi Sdn. Bhd.

 Matematik  Tingkatan 3  Jawapan Mahir KKABNADTUN! GAN

4. 1.8 × 104 1. 1 × 105
5. 2 × 104
6. 3.6 × 105 4BAB Lukisan Berskala
7. 3.2 × 104 Scale Drawings
8. 1.3 × 103
9. 8.84 × 106 A 1. (I) ✓ (II) ✓
10. 4.74 × 104 (IV)
11. 4.29 × 103 (III)
12. 9.24 × 108 n1
13. 3.818 × 1014 B 1. n1 n1 n=1
14. 2.109 × 1010 n1 n=1
15. 9.9 × 102 2. n1 n1
16. 8.5 × 101 3. n=1
17. 1.053 × 10–2
18. 1.141 × 10–4 C KʹLʹ 1 KL 2 1 : 2 1:2
19. 1.13 × 10–2
20. 8.26 × 10–3 NʹMʹ 3 NM 6 3 : 6 3 : 6 =1:2
21. 2.8 × 10–2 3 3
22. 4 × 10–4
KʹLʹ 3 KL 2 3 : 2 3 : 2 =1: 2
H 1. 32 3 3 3

2. 6.67 × 10–4 s NʹMʹ 9 NM 6 9 : 6 9 : 6 =1: 2
3. 2.03 × 102 m2 9 9 3

I 1. 9.88 × 10–2 KʹLʹ 5 KL 2 5 : 2 5 : 2 =1: 2
5 5 5
2. 1.33 × 10–4
3. 1.79 × 10–4 NʹMʹ 15 NM 6 15 : 6 15 : 6 =1: 2
15 15 5

Praktis BerfKoArNmDaUtNGPATN3 D 1. 1 : 3

1. B 2. 1 : 2
2. B 2
3. A 3. 1: 5
4. 1.05 × 10–5, 3.5 × 10–5, 6.0 × 10–5, 9.0 × 10–3
5. (a) 4 × 105 × 6 × 105 E 1. (i)

= 24 × 1010

= 2.4 × 10  11

(b) 2 × 106
5 × 103

= 0.4 × 103

= 4 × 10  2 (ii)
6. (a) 6.8 × 10–6 + 3.5 × 10–5
= 6.8 × 10  –1 × 10–5 + 3.5 × 10–5

= 0.68 × 10–5 + 3.5 × 10–5

= (0.68 + 3.5) × 10–5

= 4.18 × 10–5

(b) 7.22 × 10−7
(c) 9.4608 × 1017 cm

© Penerbitan Pelangi Sdn. Bhd. J2

STEADY! TINGKATAN TC203031bS STEADY! MATEMATIK Mathematics TINGKATAN 3 BUKU B

MATEMATIK 3

Mathematics KSSM

Siri Steady! merangkumi buku A dan buku B untuk memudahkan latih
tubi dan rujukan mengikut topik. Soalan-soalan dalam setiap subtopik
ditulis mengikut tahap penguasaan dan aras kesukaran yang berbeza
yang diakhiri praktis berformat PT3 demi membimbing murid secara
berperingkat ke arah pencapaian akademik yang cemerlang. Soalan
berelemen KBAT juga disajikan pada akhir setiap bab untuk menguji
kemahiran murid untuk
mengaplikasikan apa-apa
konsep matematik yang
telah dipelajari.

© Penerbitan Pelangi Sdn. Bhd. 2021
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