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

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

W h a t i s i t ?

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lT 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 .

Conversion Units

Take an example: 12 in = 1 ftDivide both sides by 1 ft

12 in = 1 ft = 11 ft 1 ftOR divide both sides by 12 in12 in = 1 ft = 112 in 12 inFor every equality there are 2

conversion factors.

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e l

W h a t i s g i v e nW h a t i s g i v e n A f r a c t i o nA f r a c t i o n

e q u a l t o o n ee q u a l t o o n e

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 .

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 0 0 0 g 1 p o u n d

4 5 4 g= 2 . 2 p o u n d s

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 .

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 om e t e r s / s e c o n d

6 5 m i l e s

1 h o u r

1 h o u r

3600 s e c o n d

1000 m e t e r s

0.6214 m i l e s

=

Factor label Method

Answer:65 miles per hour = 29 meters per second

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 ?

8 buses

1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 ?

8 buses 12 cars

1 bus

1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 ?

8 buses 12 cars

1 bus

1 truck

3 cars

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 ?

8 buses 12 cars

1 bus

1 truck

3 cars

1000 bballs

1 truck

F a c t o r - L a b e lF a c t o r - L a b e lF a c t o r - L a b e lF 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 .

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

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

E n d

T h eT h e

I n t e r n a t i I n t e r n a t i o n a l S y s t e mo n a l S y s t e mo f M e a s u r e m e n to f M e a s u r e m e n t

THE MEASURE OF THINGS

S I B a s e U n i t sS I B a s e U n i t s

M a s s - K i l o g r a m KgL e n g t h - M e t e r mT i m e - S e c o n d s

T e m p e r a t u r e -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 -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 -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 -L i g h t i n t e n s i t y - C a n d e l a cd

D e r i v e d U n i t sD 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 C o m b i n a t i o n o f B a s e U n i t s U n i t s

A r e a = l e n g t h A r e a = l e n g t h 22

V o l u m e = l e n g t h V o l u m e = l e n g t h 33

D e n s i t y = m a s s D e n s i t y = m a s s / / v o v o l u m el u m e

MORE DERIVED UNITS

FORCE NEWTON NPRESSURE PASCAL PaENERGY JOULE JPOWER WATT WVOLTAGE VOLT VFREQUENCY HERTZ HzELECTRIC CHARGE COULOMB C

S I P r e f i x e sS I P r e f i x e s

M e g a - 1 000 000M e g a - 1 000 000

K i l o - 1 000K i l o - 1 000

D e c i - 0 . 1D e c i - 0 . 1

C e n t i - 0 . 01C e n t i - 0 . 01

M i l l i - 0 . 001 M i l l i - 0 . 001

M i c r o - 0 . 000 001M i c r o - 0 . 000 001

N a n o - 0 . 000 000 N a n o - 0 . 000 000 001001

D i f f e r e n t V o l u m e D i f f e r e n t V o l u m e U n i t sU n i t s

L i t e r = C u b i c D e c i m e t L i t e r = C u b i c D e c i m e t e re r

M i l l i l i t e r = C u b i c C e n t M i l l i l i t e r = C u b i c C e n t i m e t e ri m e t e r

T h eT h e

I n t e r n a t i I n t e r n a t i o n a l S y s t e mo n a l S y s t e mo f M e a s u r e m e n to f M e a s u r e m e n t

E n dE n d

S i g n i f i c a n t D i g S i g n i f i c a n t D i g i t si t s

S i g n i f i c a n t D i g S i g n i f i c a n t D i g i t si 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.

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 yo f t h e m e a s u r i n g d e v i c e .

S i g n i f i c a n t D i g S i g n i f i c a n t D i g i t si 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

R u l e s t o d e t e r m R u l e s t o d e t e r m i n e s i g n i i n e s i g n i f i c a n t d i g i t sf 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 .

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.

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.

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

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

P r o p e r t i e sP r o p e r t i e s

Q u a l i t a t i v eQ 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 eQ 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 .

R e l i a b i l i t yR e l i a b i l i t y

A c c u r a c yA 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 nP 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 .

Comparison of accuracy and precision.

Low precision and accuracyLow precision and accuracy

Comparison of accuracy and precision

Accurate and preciseAccurate and precise

Comparison of accuracy and precision.

High precision low High precision low accuracyaccuracy

P e r c e n t E r r o rP 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 r r o r =

e x p v a l u e - k n o w n v a l u e

k n o w n v a l u e

S i g n i f i c a n t D i g S i g n i f i c a n t D i g i t si t s

E n dE n d

S c i e n t i f i c N o t a t i S c i e n t i f i c N o t a t i o no n

MM X X 1 0 1 0 nn

S c i e n t i f i c N o t a S c i e n t i f i c N o t a t i o nt 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 .

MM X X 1 0 1 0 nn

S c i e n t i f i c N o t a S c i e n t i f i c N o t a t i o nt 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 .

MM X X 1 0 1 0 nn

S c i e n t i f i c N o t a S c i e n t i f i c N o t a t i o nt i o n

T h e b a s i c f o r m i s :

MM X X 1 0 1 0 nn

P a r t O n e :P a r t O n e :

M h 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 .MM X X 1 0 1 0 nn

P a r t T w o aP 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 .

MM X X 1 0 1 0 nncontinued

P a r t T w o bP 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 .

MM X X 1 0 1 0 nn

continued

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 .

MM X X 1 0 1 0 - - nn

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

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

S c i e n t i f i c n o t a S c i e n t i f i c n o t a t i o n a n d y o t i o n a n d y o u r c a l c u l a t o r :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

MM X X 1 0 1 0 - - nn

S c i e n t i f i c n o t a S c i e n t i f i c n o t a t i o n a n d y o t i o n a n d y o u r c a l c u l a t o r :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

S c i e n t i f i c n o t a S c i e n t i f i c n o t a t i o n a n d y o t i o n a n d y o u r c a l c u l a t o r :u r c a l c u l a t o r :

M u l t i p l y b y t h i s n u m b e r :

2 . 5 X 1 0 - 5

T h e a n s w e r i s :

1 . 5 X 1 0 19

S c i e n t i f i c N o t a S c i e n t i f i c N o t a t i o nt i o n

E n dE n d