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L i m i t s o f a c c u r a c y                                                

B y t h e e n d o f t h e l e s s o n y o u s h o u l d b e a b l e t o :    

•        G i v e a p p r o p r i a t e u p p e r a n d l o w e r b o u n d s f o r p r e v i o u s l y r o u n d e d n u m b e r s  

•        O b t a i n a p p r o p r i a t e u p p e r a n d l o w e r b o u n d s t o

s o l u t i o n s o f p r o b l e m s .  

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 1 o f 1 3 )    

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S t a r t e r                                                                      

4 7 2 . 3      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 2 o f 1 3 )    

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A g i r l ' s h e i g h t i s g i v e n a s 1 6 2 c m c o r r e c t t o t h en e a r e s t c e n t i m e t r e .  

•        I s 1 6 1 . 7 c m a p o s s i b l e v a l u e f o r t h e g i r l ' s h e i g h t ?      

•        I s 1 6 2 . 3 5 c m a p o s s i b l e v a l u e f o r t h e g i r l ' s h e i g h t ?      

•        G i v e t w o p o s s i b l e v a l u e s f o r t h e g i r l ' s h e i g h t , l o w e r t h a n 1 6 2 c m .    

•        G i v e t w o p o s s i b l e v a l u e s f o r t h e g i r l ' s h e i g h t , b i g g e r t h a n 1 6 2 c m .    

•        W h a t i s t h e l e a s t p o s s i b l e v a l u e f o r t h e g i r l ' s h e i g h t ?      

•        I s 1 6 2 . 5 c m a p o s s i b l e v a l u e f o r t h e g i r l ' s h e i g h t ? W h y ?      

•        R e p r e s e n t b y t h e m e a n s o f a n i n e q u a l i t y a l l p o s s i b l e v a l u e sf o r t h e g i r l ' s h e i g h t .    

  1 6 1 . 5      ≤ h < 1 6 2 . 5                                                                                  

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 3 o f 1 3 )    

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1 6 1 . 5 c m          

L o w e r b o u n d         U p p e r b o u n d      N o t e t h a t t h e r e i s a n " e m p t yd o t " a t 1 6 2 . 5 . I t m e a n s t h a t

t h i s i s n o t a p o s s i b l e a n s w e rf o r o u r p r o b l e m .    

P o s s i b l e v a l u e s f o r t h e g i r l ' s h e i g h t    

1 6 2 . 5 c m          1 6 2 c m          

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 4 o f 1 3 )    

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I f y o u m a k e a m e a s u r e m e n t t o a g i v e n u n i t ,t h e t r u e v a l u e l i e s i n a r a n g e t h a t e x t e n d sh a l f u n i t b e l o w a n d h a l f u n i t a b o v e t h e

m e a s u r e m e n t .    

E x a m p l e :    

A t e m p e r a t u r e T i s g i v e n a s 3 0 0 , c o r r e c t t o t h e n e a r e s t d e g r e e .    

W r i t e d o w n a n i n e q u a l i t y t o r e p r e s e n t t h e r a n g e o f a l l p o s s i b l e

v a l u e s f o r t h e t e m p e r a t u r e T .    

2 9 . 5 0      ≤                                                         T < 3 0 . 5 0      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 5 o f 1 3 )    

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I f a n u m b e r i s r o u n d e d a s 1 6 t o t h e n e a r e s t w h o l en u m b e r , w h a t a r e t h e u p p e r a n d l o w e r b o u n d s ?      

F o r a n y v a l u e g i v e n t o t h e n e a r e s t u n i t    

i ) t h e m a x i m u m p o s s i b l e e r r o r i s h a l f o f t h a t " u n i t "    

i i ) i t s l i m i t s o f a c c u r a c y a r e t h e v a l u e ±                                                         h a l f o f t h e

" u n i t " .  

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 6 o f 1 3 )    

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 1 ) A n a n s w e r a i s g i v e n a s 4 2 t o 2 s i g n i f i c a n t f i g u r e s .  

S o t h e m a x i m u m e r r o r i s 0 . 5 ( h a l f o f 1 ) . T h e n

4 2 - 0 . 5 ≤                                                         a < 4 2 + 0 . 5      

4 1 . 5 ≤                                                         a < 4 2 . 5      

l o w e r b o u n d         u p p e r b o u n d      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 7 o f 1 3 )    

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2 ) A n n u m b e r b i s g i v e n a s 4 8 0 t o 2 s . f .  

 

T h e l i m i t s a r e 4 8 0      ±                                                         5 :  

4 7 5    ≤                                                         b < 4 8 5      

S o t h e m a x i m u m e r r o r i s 5 ( h a l f o f 1 0 )    

l o w e r b o u n d         u p p e r b o u n d      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 8 o f 1 3 )    

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3 ) A m e a s u r e m e n t m i s g i v e n a s 7 3 0 0 0 t o 2 s . f .  

 

7 2 5 0 0      ≤                                                         m < 7 3 5 0 0      

4 ) A n u m b e r p i s g i v e n a s 8 . 7 t o 1 d . p .  

  S o t h e m a x i m u m e r r o r i s 0 . 0 5 ( h a l f o f 0 . 1 ) .  

T h e n t h e l i m i t s o f a c c u r a c y w i l l b e :    

8 . 7    ±                                                         0 . 0 5      

7 . 7 5       ≤                                                         p < 8 . 7 5      

S o t h e m a x i m u m e r r o r i s 5 0 0 ( h a l f o f 1 0 0 0 ) .

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 9 o f 1 3 )    

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5 ) A n u m b e r a i s g i v e n a s 6 . 9 9 t o 2 d e c i m a l p l a c e s .  

S o t h e m a x i m u m e r r o r w i l l b e 0 . 0 0 5 ( h a l f o f 0 . 0 1 )     

6 . 9 9       ±                                                         0 . 0 0 5      

6 . 9 8 5 ≤ a < 6 . 9 9 5      

S o l v e w o r k s h e e t : " L i m i t s o f a c c u r a c y " E x . 1    

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 1 0 o f 1 3 )    

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6 ) T h e t w o s i d e s o f t h e r e c t a n g l e w e r e m e a s u r e dt o t h e n e a r e s t m m .

F i n d t h e l e a s t a n d g r e a t e s t p o s s i b l e v a l u e s o f t h e p e r i m e t e r .  

4 . 6 c m          

7 . 9 c m          

 

1 ) F i n d t h e u p p e r a n d l o w e r b o u n d s o f e a c h m e a s u r e m e n t    

7 . 8 5 ≤                                                         a < 7 . 9 5         4 . 5 5 ≤                                                         b < 4 . 6 5      

s m a l l e s t p e r i m e t e r : 2 x 7 . 8 5 + 2 x 4 . 5 5 = 2 4 . 8 c m          

g r e a t e s t p e r i m e t e r : 2        x         7 . 9 5 + 2 x         4 . 6 5 = 2 5 . 2 c m          

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 1 1 o f 1 3 )    

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7 ) C a l c u l a t e t h e u p p e r a n d l o w e r b o u n d s f o r :    

  1 7 . 8 - 4 . 2

i f e a c h o f t h e n u m b e r s i s g i v e n t o 1 d . p .  

1 7 . 8 l i e s i n t h e r a n g e :       1 7 . 7 5      ≤                                                         x < 1 7 . 8 5      

4 . 2 l i e s i n t h e r a n g e :       4 . 1 5      ≤                                                         y < 4 . 2 5      

T h e l o w e r b o u n d ( s m a l l e s t v a l u e ) o f x - y i s

o b t a i n e d w h e n w e u s e t h e s m a l l e s t v a l u e f o r x a n dt h e g r e a t e s t f o r y , s o :

m i n i m u m v a l u e : 1 7 . 7 5 - 4 . 2 5 = 1 3 . 5      

T h e u p p e r b o u n d ( g r e a t e s t v a l u e ) o f x - y i s

o b t a i n e d w h e n w e u s e t h e g r e a t e s t v a l u e f o r x a n d

t h e s m a l l e s t f o r y , s o :

m a x i m u m v a l u e : 1 7 . 8 5 - 4 . 1 5 = 1 3 . 7      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 1 2 o f 1 3 )    

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S o l v e w o r k s h e e t : " L i m i t s o f a c c u r a c y " E x . 2 - 5      

T i t l e : F e b 2 6 - 1 1 : 5 0 a . m . ( 1 3 o f 1 3 )