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

Answer:

Option D. 6.24=156/25

Step-by-step explanation:

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

$6.24=\frac{624}{100}$

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

$6.24=\frac{624/4}{100/4}\\ 6.24=\frac{156}{25}$

Answer 2

Answer:

Option C.

Step-by-step 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).

$100x-x=624.242424...-6.242424...$

$99x=618$

$x=\dfrac{618}{99}$

$x=\dfrac{203}{33}$

$x=6\dfrac{8}{33}$

Therefore, the correct option is C.