The length of a pencil is ( 15.5 +_ 0.1)cm. A small piece of length is cut out so that the length of the remaining pencil is ( 11.9 +_ 0.2) cm .What is the length of the pencil?
Ans (3.2 +_ 0.1)cm How?
+_ means plus or minus symbol

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Solution

$I n i t i a l l e n g t h o f t h e p e n c i l = 15.5 \pm 0.1 c m L_{1} = 15.5 c m e r r o r i s ∆ L_{1} = 0.1 c m F i n a l l e n g t h o f t h e p e n c i l = 11.9 \pm 0.2 c m L_{2} = 11.9 c m e r r o r i s ∆ L_{2} = 0.2 c m L e n g t h o f t h e c u t p a r t o f t h e p e n c i l = f i n a l l e n g t h - i n i t i a l l e n g t h L = L_{1} - L_{2} L = 15.5 - 11.9 L = 3.6 c m e r r o r i s : ∆ L = ∆ L_{1} + ∆ L_{2} = 0.1 + 0.2 = 0.3 c m l e n g t h o f t h e c u t p a r t = 3.6 \pm 0.3 c m$

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