Question

Terrence says pi is a rational number since it is the ratio of a circle's circumference to its diameter. Why is

Terrence incorrect?
(A
Pi cannot be written as a ratio of integers even if it represents a different ratio.
(B
Terrence is confusing the definition of rational numbers with the definition of
whole numbers.
(C
Pi can be written as a decimal with repeating digits.
(D
Terrence is confusing pi and square root of 2

Answer 1

(A) Pi cannot be written as a ratio of integers even if it represents a different ratio.

Explanation:

A rational number is can be expressed as the quotient of two integers. It can either be a number with or without a decimal part when converted to decimals.

C = 2
`\pi`r and D = 2r

C =
`\pi`D

Thus,
`\pi` =
`(C)/(D)`

=
`(22)/(7)`= 3.142857143...

Terrence was incorrect because Pi is an irrational number which cannot be represented by a simple fraction without approximation.