Form 4 Mathematics Chapter 1

Chapter 1/Bab 1 : Standard Form / Bentuk Piawai

1.1 Significant Figure / Angka Bererti

What are significant figure? Significant figures are used to denote an exact value of numbers to a certain specific degree of accuracy . For example : 289 = 300 ( correct to 1 significant figure)

Apa itu angka bererti? Angka bererti digunakan untuk menandakan nilai tepat sesuatu nombor kepada nombor yang terdekat. Contoh: 289 = 300 ( tepat kepada 1 nombor bererti)

Rules in rounding off a positive number to a given number of significant figures

Syarat-Syarat membundarkan nombor positif kepada nombor bererti yang diberi.(i) In a positive number, the non-zero digits are significant figures Untuk nombor positif , nombor bukan sifar adalah bererti

For example/contoh, 13.5 [ 3 significant figures/ 3 nombor bererti] 2756 [ 4 significant figures/ 4 nombor bererti]

(ii) If there are zero in between the non-zero digits, it is considered as significant figures too Jika terdapat sifar di antara nombor bukan sifar, ia juga dianggap nombor bererti.

For example/contoh , 105 [ 3 significant figures/3 nombor bererti] 200.8 [ 4 significant figures/ 4 nombor bererti] (iii) If a zero comes after a non-zero digit in a decimal, it is considered as significant figures also since it indicates the degree of accuracy where the measurement is taken. Jika sifar didapati selepas nombor bukan sifar dalam satu perpuluhan, ia juga dianggap nombor bererti kerana ia menandakan darjah ketepatan untuk ukuran yang diambil.

For example/contoh , 0.30 [ 2 significant figures/ 2 nombor bererti] 200.0 [ 4 significant figures/ 4 nombor bererti]

(iv) If a zeros are before a non-zero digit in a decimal which is less than 1, it is not considered as significant figures! Jika nombor sifar didapati sebelum nombor bukan sifar didalam perpuluhan yang kurang daripada 1 , ia tidak dianggap sebagai nombor bererti.

For example/ contoh , 0.0045 [ 2 significant figures/ 2 nombor bererti] 0.006005 [ 4 significant figures/ 4 nombor bererti]

(v) For the final case, if there are zeros after a non-zero digit for a whole number, it may or may not be significant figures as it depends on the degree of accuracy required Untuk kes terakhir, jika terdapat sifar selepas nombor bukan sifar untuk nombor bulat, ia mungkin / tidak mungkin menjadi nombor bererti kerana ia berganting kepada darjah ketepatan yang dikehendaki.

For example/contoh, 600 [ 1 significant figure if the degree of accuracy needed is to nearest Hundred/ 1 nombor bererti jika darjah ketepatan yang dikehendaki ialah 100] 600 [ 2 significant figures if the degree of accuracy needed is to nearest ten 2 nombor bererti jika darjah ketepatan yang dikehendaki ialah 10] 600 [ 3 significant figures if the degree of accuracy is to nearest whole number1/ 3 nombor bererti jika darjah ketepatan yang dikehendaki ialah 1]

Exercise/Latihan

1. 5675 [1 s.f/ 1 n.e]

2. 0.5273 [ 3 s.f/ 1 n.e]

3. 303.27 [2 s.f/ 1 n.e]

4. 20.568 [4 s.f/ 1 n.e]

5. 0.005613 [2 s.f/ 1 n.e]

6. 1462.02 [3 s.f/ 1 n.e]

Performing operations of addition, subtraction , multiplication and division for numbers and state the answer in the given specific significant figures

Melakukan operasi penambahan, penolakan, pendaraban and pembahagian untuk nombor & nyatakan jawapan didalam nombor bererti yang khusus.

1.56.4 6.78 + 23.45 [2 s.f/ 2 n.e]

2. 34.3 + 6.78 0.024 [3 s.f/ 3 n.e]

3. 3.08 100 x 4.5. [2 s.f/ 1 n.e]

1.2 Standard FormStandard form is used to express a very large or very small numbers in the form of A x 10n whereA is greater of equal to 1 but less than 10. For instance, 1 A < 10 and n is an integerLets look at one example.How can you express 450000000 in standard form? Very easy! Just look at the number. Observethat the number is a product of 4.5 with 108 . So the standard form of 450000000 is 4.5 x 108Example 1Express 2340000 in standard formTips : How to get to know whether this should be a positive index or a negative index ? Well,this number is large and is a multiple of a number. So, from here, we know that this is a positiveindex of 10. But to the power of what? Just move the decimal behind the 2340000. to front untilit fulfil the condition of 1 A < 10 , which is 2.34(also count how many times you move thedecimal point from back to front to get 2.34) In this case we have move the decimal point 6 times.So 2340000 is the multiple of 2.34 x 106From here, you moved 6 places to obtain 2.34. Hence,Answer : 2.34 x 106 (You can check this by typing 2.34 x 106 into your calculator and you willget 2340000 , same as for the question )Example 2 Express 0.000035 in standard form. Tips : For this case, this should have a negative index since the number is very small (which is divided by 10n),n is a positive integer. Move the decimal point to the back to get 3.5(count also the number of places you moved the decimal point) How many places the decimal point moved to the back? Its 5! So, if the decimal point is moved to the back, this should be a negative index, which is 10-5 Answer : 3.5 x 10-5 ( You can check the answer by typing 0.000035 in your calculator and you will get 3.5 x 10-5 which is the same as your final answer for this question!) Understand so far by having this two examples? Well, now we are going to convert numbers in standard form to a single number! How to convert A x 10n to a single number ? Follow these two rules ! If the index n of the power 10 is positive, moves the decimal point in A n places to the right. If the index n of the power 10 is negative, moves the decimal point in A n places to the left.

Example 3 Convert 4.37 x 106 to a single number. Tips : The index n ,which is 6 is a positive number.So, move the decimal point in 4.37 6 places to to the right.

Answer : 4.37 x 106 = = 437000 (You can check this by pressing 4.37 x 106 into your calculator and then press = . You will get the answer as 4370000! Example 4 Convert 6.78 x 10-4 to a single number. Tips : Since the index n, which is -4, is a negative number, so move the decimal point in 6.78 4 places to the left. Answer : 6.78 x 10-4 = = 0.000678 (you can type 6.78 x 10-4 into your calculator and press shiftENG,do this TWICE, you will get 0.000678 x 100 as your answer)

Example 5Evaluate the value of 3400 0.0012 , correct it to 2 significant figures and expressit in standard form.Tips : Do it one by one, change the answer according to the significant figuresneeded and then express it in standard form.Answer : By pressing calculator, you will get 3400 0.0012 = 2833333.333. Now,correct 2833333.333 to 2 significant figures using the knowledge you have learntin subtopic 1.1,you will get the answer as 2800000. 2800000 is a multiple of 106for 2.8 and hence the final answer is 2.8 x 106 ( Well, you can check your answerby calculator again by pressing 2.8 x 106 and you will eventually get 2800000 asyour answer! Thats easy! But remember to express your final answer as 2.8 x 106(as required by question)