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This document provides information about units, prefixes, and formulas in the metric system. It includes: 1. Explanations of the seven base SI units - meter, kilogram, second, ampere, kelvin, mole, and candela. 2. Descriptions of the prefixes used to denote powers of ten when multiplying or dividing units, such as kilo (103) and milli (10-3). 3. Examples of calculations using prefixes to convert between units, like converting 4,700,000,000 meters to 4,700 kilometers. The document also contains sections on error analysis in measurements, kinematic formulas, and dimensional analysis.
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- 2. – F ˆF www.schoolDD.com 1 1 ˈ F ʽ F F F F F F F F F F F F F F F F F F ˈ F ʽ F 1.1 ʽ F F ʽ F F F F ʽ F ˈ F F F F F F F F ˈ F F F F F F F F F F F F F F F F F F ʽ F ˈ F F F 1.2 F SI F 7 F F F (m), (kg), (s), F (A), (K), (mol) (cd) F F F F F F (N) = kg.m/s2 , (J) = N.m = kg.m2 /s2 1.3 F F (Prefix) F F F F F F F F F F 1 F F 1000 ˈ F F F F 1000 103 F F F F F F F (1012 ), (10-12 ), (109 ), (10-9 ), (106 ), (10-6 ) (103 ), (10-3 ), (102 ), (10-2 ), (101 ), (10-1 ) F F F F F ˈ F ˈ F F , , , , , F F F
- 3. – F ˆF www.schoolDD.com 2 F F F F 103 F F 103 F 106 109 1012 F F F 101 F 102 101 F F ˈ F F ... F ˈ .... 1012 10-12 109 10-9 106 10-6 103 10-3 102 10-2 101 10-1 F 1 F . 4,700,000,000 F ˈ F F F 1 = 106 F ˈ (10-6 x 106 ) F F 1 F F F ... ∴ 4,700,000,000 x (10-6 x 106 ) = 4,700 x 106 = 4,700 Mm Ans . F F F F 0.0004 F 1 = 10-3 ∴ 0.0004 x (103 x 10-3 ) = 0.4 x 10-3 = 0.4 mm Ans . 0.5 1 = 103 ∴ 0.5 = 0.5 x 10-3 = 0.5 x 10-3 x (10-3 x 103 ) = 0.5 x 10-6 x 103 = 0.5 x 10-6 kg Ans . 1 , 1 = 10-2 ∴ (1 )2 = (10-2 )2 = 10-4 2 1 = 10-4 Ans
- 4. – F ˆF www.schoolDD.com 3 1 F F 101 (1 )2 = (101 )2 = 102 2 1 = 102 Ans F F F Hard Disk F , F F ? 1.4 F 1. F F F F F F F F F F s = ut + ଵ ଶ at2 F F m = ୫ ୱ x s + ୫ ୱమ x s2 F m = m + m 2. F F F ˈ F F F F F F F a = ୴ି୳ ୲ F F ୫ ୱమ = ౣ ౩ ି ౣ ౩ ୱ F ୫ ୱమ = ୫ ୱమ F F F F T = 2πට ℓ F F s = ට ୫ ౣ ౩మ = √sଶ F s = s 1.5 F F (error) F F F F F A ˈ F F A ˈ F + A ˈ A + A F F F F F 70 + 0.2 F F ˈ F F F 69.8 70.2
- 5. – F ˆF www.schoolDD.com 4 - F F R = A +/- B R = A + B F = ( A +/- B ) + ( A + B ) F R = A +/- 2B R = A + 2 B F = ( A +/- 2B ) + ( A + 2 B ) - F F (%) F F F (%) F F R = A x/ൊ B R = ( x100 + x100 ) % F = ( A x/ൊ B ) + ( x100 + x100 ) % F R = A x/ൊ B2 R = ( x100 + ଶ x100 ) % F = ( A x/ൊ B2 ) + ( x100 + ଶ x100 ) % F R = A x/ൊ √B R = ( x100 + ଶ x100 ) % F = (A x/ൊ √B ) + ( x100 + ଶ x100 ) % F 2 F 12.44 + 0.01 . F ˈ 2 F F 4.52 + 0.02 F F F F R = A B F F R = ( A B ) + ( A + B )
- 6. – F ˆF www.schoolDD.com 5 = ( 12.44 - 4.52 ) + ( 0.01 + 0.02 ) R = 7.92 + 0.03 ∴ F F = 7.92 + 0.03 . Ans F 3 F ˈ F F 1.20 + 0.01 ˈ F F ˈ F F V = W x L x H F F V = (W x L x H ) + ( x100 + x100 + ୌ ୌ x100 ) % = (1.20 x 1.20 x 1.20) + ( .ଵ ଵ.ଶ x100 x 3 )% = 1.73 + 2.5 % V = 1.73 + ( ଵ.ଷ ୶ ଶ.ହ ଵ ) F V = 1.73 + 0.043 3 Ans + 0.043 ˈ 2.5 % Ans F 4 F F F (ℓ) ˈ 40.0 + 0.2 . F F F T = 2πට ℓ F F ( g = 10 m/s2 ) T = 2πට ℓ F F T = 2πට ℓ + ( ℓ ଶℓ x 100 ) % = 2 x (22/7) x ට .ସ ଵ + ( .ଶ ଶ୶ସ x 100 ) % = 1.256 + 0.25 % T = 1.256 + ( ଵ.ଶହ ୶ .ଶହ ଵ ) F F T = 1.256 + 0.003 s Ans
- 7. – F ˆF www.schoolDD.com 6 F 5 F F F 1.00 + 0.01 F F ˈ F F V = 4/3 x π x (d/2)3 F F V = 4/3 x π x (d/2)3 + ( ଷ ୢ ୢ x 100 ) % = 4/3 x (22/7) x (1.00 /2 )3 + ( ଷ ୶ .ଵ ଵ. x 100 ) % = 0.523 + 3 % V = 0.523 + ( .ହଶଷ ୶ ଷ ଵ ) V = 0.523 + 0.02 m3 Ans ˈ 3 % Ans 1.6 F . + . F F F F 6 F 4.25 + 0.01 . F F 4.2 ( ) 5 0.1 . F 0.01 . F ˈ F F F 4.24 . 4.26 . 1 2 3 4 5 6 F F 4.2 + F 0.05 = 4.25
- 8. – F ˆF www.schoolDD.com 7 1. F F F F F 0 F F F 0.671 , 4.03 , 0.043 , 20.00 , 0.40 , 0.0003 3 , 3 , 2 , 4 , 2 1 2. F F F F F F 0 F F 15 , 136 , 4245 , 70324 , 2001 2 , 3 , 4 , 5 4 3. F F F F 0 F A x 10n 1 A ൏ 10 10n F ˈ F 12000 F ˈ 1.2 x 104 , 1.20 x 104 , 1.200 x 104 , 1.2000 x 104 2, 3, 4, 5 F F F F F 3.21 + 4.156 = 7.366 ˈ 7.37 ( F 3 5 ˆ F F 5 ˆ ) 5354 - 21.6 = 5332.4 ˈ 5332 F F F F F 2.34 x 100.9 = 236.106 ˈ 236 7.3 ÷ 874 = 0.0083524 ˈ 0.0084 537.13 x 4.5 = 2417.085 ˈ 2.4 x 103 1.7 F F F F F ˈ F F F y = mx + c x ˈ y ˈ ˈ y ˈ x F m = y/ x c ˈ y (y x F y2 , y½ , 1/y x2 , x ½ , 1/x F ) F F F F F ˈ F F F F F F F F F c x y = mx + c y F y = mx + c x xy = k y = ୩ ୶ y F y = ௫ k F
- 9. – F ˆF www.schoolDD.com 8 1.8 F ʽ F ʽ F F F F F F ʽ F F F F ˈ ˈ F F F ˆ F ʽ F F F F ˈ ʽ F 1.8.1 F F F F F F F F F C c F 2 F ോോ F F F a a a ∆ F F = 180/3=60° a/b = A/B a/c = A/C b/c = B/C B A θ b a θ θ θ θ θ α α α α ∆ F 180° θ 90-θ θ θ θ θ
- 10. – F ˆF www.schoolDD.com 9 1.8.2 F α θ b a c F sin , cos , tan sinθ = ୟ ୡ sinα = ୠ ୡ cosθ = ୠ ୡ cosα = ୟ ୡ tanθ = ୟ ୠ tanα = ୠ ୟ tanθ = ୱ୧୬ ୡ୭ୱ sin2 θ + cos2 θ = 1 √2 60 30 √3 1 2 45 1 1 53 37 4 3 5 (slope) = ୷మି୷భ ୶మି୶భ = tan θ x y (+) x y (-) x y x y 1>2>3 3 =0 4 ˈ - 4 3 2 1 x y x y F =(k)xy c2 = a2 +b2 c = √aଶ bଶ x y y =mx + c F c y θ (x1 , y1) (x2 , y2) x y
- 11. – F ˆF www.schoolDD.com 10 1.8.3 F 1. ଵ ୟ౮ = a-x , ax .ay = a(x + y) , ୟ౮ ୟ౯ = ax .a- y = a(x - y) , a0 = 1 2. F log a = x F a = 10x F ln a = x F a = ex log(a.b) = log a + log b log(a/b) = log a - log b 1.8.4 1. F ax2 + bx + c = 0 F x = ିୠേ√ୠమିସୟୡ ଶୟ 2. F x2 a2 = 0 (x a)(x + a) = 0 F x = +a x = -a 3. F (x a)2 = 0 x2 2ax + a2 = 0 (x a)(x - a) = 0 F x = +a 4. F (x + a)2 = 0 x2 + 2ax + a2 = 0 (x + a)(x + a) = 0 F x = -a 5. F x2 - 4 x - 12 = 0 (x - 6)(x + 2) = 0 F x = 6 , -2 1.8.5 F 1. 5 = (3+t)2 5-3 = 2t or 2. y = 3x + 2√3 x y = 5√3 x or 3. 2x3 = 4x2 - (3x + x2 )x x F ? 4. y = 3x + 2 x y F ? 1.8.6 F F 1. F a ן b ୟభ ୟమ = ୠభ ୠమ 2. F a ן ଵ ୠ ୟభ ୟమ = ୠమ ୠభ 3. F A x B = C x D A < C F B > D 4. D ଡ଼ = P F F F X F F F F ? 5. A ହమ େିଵ = (N ଵ ଶ ) X A ଷమ େିଵ = (6 - N) Y F N = 3 F X ˈ F Y ?
- 12. – F ˆF www.schoolDD.com 11 1.8.7 F F F ˈ F F ˆ F F F F F F F F ˆ F F F F ˈ F ʾ F ˈ 44 ʾ F F F 5 ʾ F F 2 ʾ F ˆ F F F ˆ = A ʾ F = B ʾ = C ʾ ʾ F ˈ 44 ʾ F ˆ ˈ 44+1+1+1 = 47 ʾ F F F A + B + C = 47 ----(1) F F F 5 ʾ F F F B - A = 5 ----(2) F F 2 ʾ F F F B - C = 2 ----(3) F F F F F 3 3 F F F F F F 3 A C F B (1) + (2) + (3) , (A+B+C) + (B-A) + (B-C) = 47 + 5 + 2 3B = 54 B = 18 F B (2) F A F B - A = 5 18 - A = 5 18 - 5 = A A = 13 F B (3) F C F B - C = 2 18 - C = 2 18 - 2 = C C = 16 ˆ F 13, 18 16 ʾ Ans F F F F F F F ˇ F ʽ F F ! F F F F F F F F F F ˆ ʽ F F