Final answer:
To turn the decimal .16 (6 repeating) into a simplified fraction, multiply both sides by 100 to eliminate the decimal, subtract the two equations, and divide by 99.
Step-by-step explanation:
To turn the decimal .16 (6 repeating) into a simplified fraction, we can use the concept of repeating decimals. Let x be the repeating decimal .16 (6 repeating). Then, we can multiply both sides of the equation by 100 to eliminate the decimal:
x = .16 (6 repeating)
100x = 16.66 (6 repeating)
Now, we can subtract the two equations:
100x - x = 16.66 (6 repeating) - .16 (6 repeating)
99x = 16.5
Dividing both sides by 99 gives us
x = 16.5/99
Therefore, the simplified fraction is 16.5/99.