Question

Which statement shows that 6.24 is a rational number? A. 6.24 = 6.242424 B. 6.24 = 6.24 C. 6.24 = 68⁄33 D. 6.24 = 66⁄25

Answer 1

Option C.

Explanation:

Rational number: If a number expressed as p/q, where p and q are integers and q≠0.

Consider the given number is

`6.\overline{24}`

It can be rewritten as

`x=6.\overline{24}`

`x=6.242424...` ... (1)

Multiply both sides 100.

`100x=624.242424...` ... (2)

Subtract (1) from (2).

`100x-x=624.242424...-6.242424...`

`99x=618`

`x=(618)/(99)`

`x=(203)/(33)`

`x=6(8)/(33)`

Therefore, the correct option is C.

Answer 2

Option D. 6.24=156/25

Explanation:

A number is rational if we can write it as a fraction:

`6.24=(624)/(100)`

Simplifying the fraction dividing the numerator and the denominator by 4:

`6.24=(624/4)/(100/4)\\ 6.24=(156)/(25)`