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Question
The length and breadth of a rectangular sheet are 16.2 cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is ______.
Options
164 ± 3 cm2
163.62 ± 2.6 cm2
163.6 ± 2.6 cm2
163.62 ± 3 cm2
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Solution
The length and breadth of a rectangular sheet are 16.2 cm and 10.1cm, respectively. The area of the sheet in appropriate significant figures and error is `underline(164 ± 3 cm^2)`.
Explanation:
Given, Length `l = (16.2 +- 0.1)` cm
Breadth `b = (10.1 +- 0.1)` cm
Area = `A = l xx b`
= (16.2 cm) × (10.1 cm)
= 163.62 cm2
Rounding off to three significant digits, area A = 164 cm2
`(ΔA)/A = (Δl)/l + (Δb)/b = 0.1/16.2 + 0.1/10.1`
= `(1.01 + 1.62)/(16.2 xx 10.1)`
= `2.63/163.62`
⇒ `ΔA = A xx 2.63/163.62`
= `163.62 xx 2.63/163.62`
= 2.63 cm2
ΔA = 3 cm2 .......(By rounding off to one significant figure)
∴ Area, A = A ± ΔA = (164 ± 3) cm2.
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