Question

How do you write -4.16 repeating as a fraction?

a) -208/51
b) -52/13
c) -26/5
d) -13/3

Answer 1

To write -4.16 repeating as a fraction, we can multiply by 100 to eliminate the repeating part and then solve for x. The fraction -420.32/99 is equivalent to -4.16 repeating.

Step-by-step explanation:

To write -4.16 repeating as a fraction, we can use the method of converting repeating decimals to fractions. Let x equal -4.16 repeating. We multiply both sides of the equation by 100 to get 100x = -416.16 repeating. Next, we subtract x from 100x to get 99x = -416.16 repeating - x. We can align the decimal points and subtract to get 99x = -416.16 - 4.16 = -420.32. Finally, we divide both sides by 99 to get x = -420.32/99. The fraction -420.32/99 is equivalent to option b) -52/13.