Change the decimal to a fraction: 0.123123123….
A. 123/999
B. 1 23/100
C. This decimal is Irrational and cannot be written as a fraction
D. 12 13/10
E. 123/1000
To convert the decimal 0.123123123... to a fraction, we can assign it the variable x and subtract it from 10x:
x = 0.123123123...
10x = 1.231231231...
Now we can subtract the first equation from the second equation to eliminate the repeating decimal:
10x - x = 1.231231231... - 0.123123123...
9x = 1.108108108...
Simplifying both sides of the equation:
9x = 1 + 0.108108108...
9x = 1.108108108...
To get rid of the decimal in 0.108108108..., we can assign it the variable y and subtract it from 10y:
y = 0.108108108...
10y = 1.081081081...
Again, we can subtract the first equation from the second equation:
10y - y = 1.081081081... - 0.108108108...
9y = 0.972972972...
Simplifying both sides of the equation:
9y = 0.972972972...
9y = 0.972972972...
Now we can solve for y:
9y = 0.972972972...
y = 0.972972972... / 9
y = 0.108108108...
Since y is equal to 0.108108108..., and we assigned the original repeating decimal x to be equal to this value, we can substitute y back into the equation for x:
9x = 1 + y
9x = 1 + 0.108108108...
9x = 1.108108108...
Now we can solve for x:
9x = 1.108108108...
x = 1.108108108... / 9
x = 0.123123123...
Therefore, the decimal 0.123123123... can be written as the fraction 123/999.
A. 123/999 is the correct answer.