Find a whole number x in x/113 so that the ratio is a better estimate for π than the two given approximations.

The whole number x is 355

Step-by-step explanation:

* Lets explain how to solve the problem

- The whole number x in x/113 is the better estimate for π than

  the two approximated values of π ⇒ 22/7 and 3.14

- To find the whole number x lets equate the ratio by 3.14 and 22/7

∵ x /113 = 3.14

- By using cross multiplication

∴ x = 113 × 3.14

∴ x = 354.82

∵ x /113 = 22/7

- By using cross multiplication

∴ x = (113 × 22)/7

∴ x = 355.14

- x is a whole number between these two values

∵ 354.82 < x < 355.14

∴ x = 355

- Now lets check the ratio , 3.14 , 22/7 with π

∵ 355/113 = 3.14159292

∵ 22/7 = 3.142857143

∵ π = 3.141592654

∵ 355/113 and π have 6 common decimals but 22/7 and 3.14

  have only 2 common decimals with π

∴ The ratio 355/113 is the better estimate for π

∴ The whole number x is 355