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Chapter 1: 16 (page 28)

Express each approximation of 蟺 to six significant figures: (a) 22/7 and (b) 355/113. (c) Are these approximations accurate to that precision?

Short Answer

Expert verified

(a)The six significant figures of 22/7 is 3.14285

(b)The six significant figures of 22/7 is 3.14159.

(c) The approximation 355/113 is more accurate than 22/7.

Step by step solution

01

Significant figures

The significant figures of a value is the numbers that are necessary and reliable.

Part (a)

The significant figures can be calculated as,

227=3.14285

Thus, the six significant figures of 22/7 is 3.14285.

02

Calculation

Part (b)

The significant figures can be calculated as,

355113=3.14159

Thus, the six significant figures of 355/113 is 3.14159.

Part (c)

Since the accurate value of 蟺 up to six significant figures is 3.14159, therefore the approximation of 355/113 is more accurate than 22/7.

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