Question

Rewrite as a simplified fraction 3.48 repeating _________.

A) 348/100
B) 348/99
C) 348/98
D) 348/97

Answer 1

The simplified fraction for 3.48 repeating is found by setting x equal to the repeating decimal, multiplying by 100 to shift the decimal, subtracting the original from the new equation, and then dividing by 99 to solve for x. The simplified fraction is 348/99. The correct answer is option B.

Step-by-step explanation:

To rewrite 3.48 repeating as a simplified fraction, we can follow these steps:

1. 
   
2. Let x equal the repeating decimal, x = 3.484848...
3. 
   
4. Multiply both sides of the equation by 100 to shift the decimal two places to the right: 100x = 348.484848...
5. 
   
6. Subtract the original x from the new equation to get rid of the repeating decimals: 100x - x = 348.484848... - 3.484848... which simplifies to 99x = 345.
7. 
   
8. Divide both sides of the equation by 99 to solve for x: x = 345 / 99.

Therefore, the simplified fraction for 3.48 repeating is 348/99, which corresponds to option B) 348/99.