Question

Write the rational number 2.13 repeating as the ratio of two integers

Answer 1

104/45 or 2 14/45

Explanation:

I got this directly from Khan Academy when I did it

(This answer is for the 13 repeating in the 2.13)

Answer 2

Let

x = 2.131313... Equation 1

Multiply both sides by 100 to get:

100x = 213.131313... Equation 2

Subtract equation 1 from equation 2.

99x = 211

x = 211/99

Answer: 211/99