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F a c t o r - L a b e l M e t h o d

F a c t o r - L a b e l M e t h o d. W h a t i s i t ?. F a c t o r - L a b e l. T h e m o s t i m p o r t a n t m a t h e m a t i c a l p r o c e s s i n c h e m i s t r y .

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F a c t o r - L a b e l M e t h o d

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  1. F a c t o r - L a b e l M e t h o d W h a t i s i t ?

  2. F a c t o r - L a b e l T h e m o s t i m p o r t a n t m a t h e m a t i c a l p r o c e s s i n c h e m i s t r y . T r e a t s n u m b e r s a n d u n i t s e q u a l l y . M u l t i p l y w h a t i s g i v e n b y f r a c t i o n s e q u a l t o o n e t o c o n v e r t u n i t s .

  3. Conversion Units • Take an example: 12 in = 1 ft • Divide both sides by 1 ft • 12 in = 1 ft = 1 • 1 ft 1 ft • OR divide both sides by 12 in • 12 in = 1 ft = 1 • 12 in 12 in • For every equality there are 2 conversion factors.

  4. F a c t o r - L a b e l A f r a c t i o n e q u a l t o o n e W h a t i s g i v e n

  5. F a c t o r - L a b e l C o n v e r t 1 0 0 0 g r a m s t o p o u n d s .

  6. F a c t o r - L a b e l C o n v e r t 1 0 0 0 g r a m s t o p o u n d s 1 p o u n d 1 0 0 0 g = 2 . 2 p o u n d s 4 5 4 g

  7. F a c t o r - L a b e l C o n v e r t 6 5 m i l e s / h o u r t o m e t e r s / s e c o n d .

  8. F a c t o r - L a b e l C o n v e r t 6 5 m i l e s / h o u r t o m e t e r s / s e c o n d = 1 h o u r 3600 s e c o n d 6 5 m i l e s 1 h o u r 1000 m e t e r s 0.6214 m i l e s

  9. Factor label Method • Answer: • 65 miles per hour = 29 meters per second

  10. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck

  11. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck 8 buses

  12. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck 12 cars 8 buses 1 bus

  13. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 12 cars 1 truck 8 buses 3 cars 1 bus

  14. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1000 bballs 12 cars 1 truck 8 buses 1 truck 1 bus 3 cars

  15. F a c t o r - L a b e l 3 2 0 0 0 b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s .

  16. F a c t o r - L a b e l M e t h o d E n d

  17. T h eI n t e r n a t i o n a l S y s t e mo f M e a s u r e m e n t THE MEASURE OF THINGS

  18. S I B a s e U n i t s M a s s -K i l o g r a m Kg L e n g t h -M e t e r m T i m e -S e c o n d s T e m p e r a t u r e -K e l v i n K A m o u n t o f s u b s t a n c e -M o l e mol E l e c t r i c c u r r e n t -A m p e r e I L i g h t i n t e n s i t y -C a n d e l a cd

  19. D e r i v e d U n i t s C o m b i n a t i o n o f B a s e U n i t s A r e a = l e n g t h 2 V o l u m e = l e n g t h 3 D e n s i t y = m a s s / v o l u m e

  20. MORE DERIVED UNITS • FORCE NEWTON N • PRESSURE PASCAL Pa • ENERGY JOULE J • POWER WATT W • VOLTAGE VOLT V • FREQUENCY HERTZ Hz • ELECTRIC CHARGE COULOMB C

  21. S I P r e f i x e s M e g a - 1 000 000 K i l o - 1 000 D e c i - 0 . 1 C e n t i - 0 . 01 M i l l i - 0 . 001 M i c r o - 0 . 000 001 N a n o - 0 . 000 000 001

  22. D i f f e r e n t V o l u m e U n i t s L i t e r = C u b i c D e c i m e t e r M i l l i l i t e r = C u b i c C e n t i m e t e r

  23. T h eI n t e r n a t i o n a l S y s t e mo f M e a s u r e m e n t E n d

  24. S i g n i f i c a n t D i g i t s

  25. S i g n i f i c a n t D i g i t s A s i g n i f i c a n t d i g i t i s o n e w h i c h i s a c t u a l l y m e a s u r e d! It includes the certain digits and the estimated digit of the measurement.

  26. Significant digits T h e n u m b e r o f s i g n i f i c a n t d i g i t s i n a m e a s u r e m e n t d e p e n d s o n the a b i l i t y o f t h e m e a s u r i n g d e v i c e .

  27. S i g n i f i c a n t D i g i t s W h e n a c a l c u l a t i o n i n v o l v e s n u m b e r s w i t h d i f f e r e n t s i g n i f i c a n t d i g i t s , t he a n s w e r c a n h a v e n o m o r e s i g n i f i c a n t d i g i t s t h a n t h e l e a s t u s e d i n t h e c a l c u l a t i o n . 3.05m X 2.10 m X 0.75 m = 4.8 m3

  28. R u l e s t o d e t e r m i n e s i g n i f i c a n t d i g i t s 1. D i g i t s o t h e r t h a n z e r o a r e a l w a y s s i g n i f i c a n t . 2. F i n a l z e r o s a f t e r a d e c i m a l p o i n t a r e a l w a y s s i g n i f i c a n t . 3. Z e r o s b e t w e e n t w o o t h e r s i g n i f i c a n t d i g i t s a r e a l w a y s s i g n i f i c a n t . 4. Z e r o s u s e d o n l y t o s p a c e t h e d e c i m a l a r e n o t s i g n i f i c a n t .

  29. FIND THE NUMBER OF SIGNIFICANT DIGITS • If a decimal point is present count from the left to the first non-zero digit. All digits after that are significant. • 0.057 010 g. Ans. 5 sig.Digs. • // / / /. • 0.057 010 g.

  30. Find the number of significant digits • If a decimal point is absent, count from the right to the first non-zero digit. All digits from here to the end are significant. • 3500 v. • // • Ans. 2 sig. Digs.

  31. Practice problems • Count the number of significant digits in the following examples: • (a) 0.0027 6701 m • (b) 19.0550 kg • (c) 3500 V • (d) 1,809,000 L

  32. Practice Problems • A number like 100.ml, with a decimal point to the right has 3 significant digits. If no decimal point is present as in 100 ml, it will have one significant digit. Count these: • (a.) 350. cm (d.) 50 dl • (b.) 2500. km (e.) 27. g • (c.) 12000 mm (f.) 101 dm

  33. P r o p e r t i e s Q u a l i t a t i v e- A p r o p e r t y w i t h o u t m e a s u r e m e n t s . Q u a n t i t a t i v e- A p r o p e r t y i s d e s c r i b e d b y a n u m b e r and a s t a n d a r d u n i t o f m e a s u r e m e n t .

  34. R e l i a b i l i t y A c c u r a c y- H o w c l o s e a m e a s u r e m e n t i s t o t h e accepted or t r u e v a l u e o f t h e q u a n t i t y . P r e c i s i o n- H o w c l o s e a s e t o f m e a s u r e m e n t s f o r a q u a n t i t y a r e t o o n e a n o t h e r , r e g a r d l e s s o f w h e t h e r t h e y a r e c o r r e c t .

  35. Comparison of accuracy and precision. Low precision and accuracy

  36. Comparison of accuracy and precision Accurate and precise

  37. Comparison of accuracy and precision. High precision low accuracy

  38. P e r c e n t E r r o r C o m p a r i s o n o f a n e x p e r i m e n t a l v a l u e t o a k n o w n v a l u e . e x p v a l u e - k n o w n v a l u e % e r r o r = k n o w n v a l u e

  39. S i g n i f i c a n t D i g i t s E n d

  40. S c i e n t i f i c N o t a t i o n MX 1 0 n

  41. S c i e n t i f i c N o t a t i o n U s e d t o r e p r e s e n t v e r y l a r g e o r v e r y s m a l l n u m b e r s . MX 1 0 n

  42. S c i e n t i f i c N o t a t i o n T h e r e a r e t w o p a r t s t o a n u m b e r e x p r e s s e d i n s c i e n t i f i c n o t a t i o n . MX 1 0 n

  43. S c i e n t i f i c N o t a t i o n T h e b a s i c f o r m i s : MX 1 0 n

  44. P a r t O n e : Mh a s a s i n g l e d i g i t t o t h e l e f t o f t h e d e c i m a l w i t h d i g i t s t o t h e r i g h t o f t h e d e c i m a l r e p r e s e n t i n g a n y o t h e r s i g n i f i c a n t d i g i t s . MX 1 0 n

  45. P a r t T w o a : n i s a n i n t e g e r r e p r e s e n t i n g t h e n u m b e r o f p l a c e s t o m o v e t h e d e c i m a l p o i n t . MX 1 0 n continued

  46. P a r t T w o b : I f n i s p o s i t i v e m o v e t h e d e c i m a l p o i n t t o t h e r i g h t . T h e n u m b e r i s g r e a t e r t h a n o n e . MX 1 0 n continued

  47. I f n i s n e g a t i v e , m o v e t h e d e c i m a l p o i n t t o t h e l e f t . T h e n u m b e r i s l e s s t h a n o n e . MX 1 0 - n

  48. 6 0 0 0 0 0 0 0 0 . 0 0 0 0 0 5 1 2 5 0 0 0 6 X 10 7 5 X 10 -6 1 . 2 5 X 10 5 W r i t e t h e f o l l o w i n g i n s c i e n t i f i c n o t a t i o n

  49. S c i e n t i f i c n o t a t i o n a n d y o u r c a l c u l a t o r : • E n t e r M • E E o r E X P • E n t e r n • I f n i s n e g a t i v e , c h a n g e s i g n MX 1 0 - n

  50. S c i e n t i f i c n o t a t i o n a n d y o u r c a l c u l a t o r : E n t e r t h i s n u m b e r i n y o u r c a l c u l a t o r : 6 . 0 2 X 1 0 2 3

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