16 - University Physics with Modern Physics

Question

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

Step-by-Step Solution

Answer

(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.

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,

$\frac{22}{7}=3.14285$ 

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

 

Calculation

Part (b)

The significant figures can be calculated as,

$\frac{355}{113}=3.14159$

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

Part (c)

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