1.1 significant figures

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Modul PdP Matematik Tingkatan 4 (Chapter 1: Standard Form)

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1.1 significant figures

  1. 1. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 1.1a Concept of significant figures Significant figures: The relevant digit of an integer or decimal number rounded off to a value according to a particular level of accuracy Properties used as a guide to round off a number to the required number of significant figures Properties Examples 1. All non-zero digits are significant 42 (2 significant figures) 62.29 (4 significant figures) 2. Zeros between non-zero digits are significant 2.08 (3 significant figures) 2006 (4 significant figures) 3. Zero following a non-zero digit in a whole number may or may not be significant. It depends on how the estimation is made *All zeros after any non-zero digit in a whole number are not significant unless stated otherwise 20 (1 significant figures) 200 (1 significant figures) 2000 (2 significant figures) 2000 (3 significant figures) 4. For decimals less than 1, zeros preceding the first non-zero are not significant *All zeros before any non-zero digit in a decimal point are not significant 0.8 (1 significant figures) 0.08060 (4 significant figures) 5. Zeros following a non-zero digit after the decimal point are significant *All zeros after any non-zeros digit in a decimal are significant 3.60 (3 significant figures) 26.00 (4 significant figures) 1
  2. 2. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 PRACTICE 1. State the number of significant figures in each of the following numbers: (a) 6050 (d) 0.600078 (b) 7.100 (e) 30.09 (c) 0.0280 (f) 80 004 2. State the number of significant figures in each of the following numbers: (a) 876 (d) 0.0802 (b) 294.02 (e) 2.020 (c) 8.0 (f) 600 2
  3. 3. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 1.1b Round off a positive number to a given number of significant figures Determine digit (x) to round off NO Is it the number after x greater or less than 5? x does not change YES Add 1 to x Is it extra digits after x located before or after decimal point? AFTER Dropping the extra digits BEFORE Change the extra digits with zero PRACTICE 1. Round off the following numbers to: (i) Correct to 3 significant figures (ii) Correct to 2 significant figures (iii) Correct to 1 significant figures (a) 38 106 (d) 45.465 (g) 0.09707 (j) 59.593 (b) 4398.7 (e) 80.043 (h) 0.0002938 (k) 598.3 (c) 1998 (f) 0.03562 (i) 0.9997 (l) 0.003498 3
  4. 4. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 2. Round off the following, correct to 3 significant figures. (a) 6.229 (d) 8996 (g) 0.006497 (b) 99.45 (e) 0.8429 (h) 0.02096 (c) 709.3 (f) 0.06025 3. Round off each of the following numbers to the number of significant figures indicated in brackets: (a) 78 534 (1) (b) 0.604 (2) (c) 4768 (2) (d) 0.003745 (3) 4
  5. 5. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 1.1c Operations involving a few numbers and significant figures Find the value of each of the following, stating your answer correct to 2 significant figures. (a) 7.5 + 0.48 ÷ 0.04 (b) 0.06 x 0.1 + 35.6 ÷ 50 (c) 6.84 ÷ 30 + 3.75 (d) 5.28 – 7.5 x 0.04 (e) (724 + 25.1) ÷ 0.2 5
  6. 6. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 (f) 1.24 ÷ 0.4 + 0.8 x 4.2 (g) 0.06 x 0.4 + 0.084 ÷ 0.2 (h) 19.2 – 4.2 ÷ 0.5 + 9.1 (i) 0.21 + 4.1 x 5 – 6.5 6
  7. 7. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 Find the value of each of the following, stating your answer correct to 3 significant figures. (a) 9.658 x 3.2 + 6.248 (b) 1.254 ÷ 0.03 – 6.2549 (c) 85.22 x 0.0663 – 76.369 (d) (e) 15.624 0.4 850 25 𝑥 32 7
  8. 8. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 Find the value of each of the following and express each answer correct to the number of significant figures indicated in the brackets (a) 0.028 ÷ 0.02 – 1.204 [3] (b) 0.68 ÷ 0.2 – 0.296 [3] (c) 0.3 x 0.04 + 1.074 ÷ 60 [2] (d) 5.2 x 0.3 – 0.345 [3] (e) 6.78 ÷ 10 x 3.1 [3] 8
  9. 9. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 (f) 0.3(4 – 0.38) [2] (g) 1.38 + 8.13 ÷ 0.3 [2] (h) 58.72 – 24.13 x 2.2 [2] (i) 0.6 x 0.8276 ÷ 0.12 [1] (j) 36.7 + 10.6 x 0.3 [2] 9
  10. 10. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 1.1d Solve problems involving significant figures 1. The height of the Petronas Twin Towers is about 451.9 m and each has 88 storeys. What is the average height of a storey? Give your answer, correct to 3 significant figures. 2. The width of a piece of land is 12.5 m and its length is twice its width. Calculate the area of the land, correct to 2 significant figures. 3. Mary borrows RM63 000 from a bank with an interest rate of 6.25% per annum. Calculate the interest she needs to pay after two years (simple interest). State your answer, correct to 3 significant figures. 4. The length of a piece of rectangular card is 15.7 cm. its width is 12.4 cm. calculate the area, in cm2, of this card, correct to 3 significant figures. 5. The volume of a cylinder is 54.5 cm3. The radius of the base is 3 cm. calculate the height of the 22 cylinder, correct to 2 significant figures. (Take 𝜋 = 7 ) 10
  11. 11. 1.1 SIGNIFICANT FIGURES MATHEMATICS FORM 4 6. The length, breadth and height of a rectangle are 7.5 cm, 12.5 cm and 10.5 cm respectively. Calculate the volume of rectangle, stating your answer correct to 4 significant figures. 7. A box contains 6 cans. Each can has a mass of 505 g. the box has a mass of 60 g. find the total mass, in g, of 6 cans and the box, stating your answer correct to 2 significant figures. 8. The diameter of a sphere is 8.45 cm. calculate its volume, in cm3, correct to 2 significant figures. 4 [ Volume of sphere = 3 𝜋r3 and use 𝜋 = 3.142 ] 11

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