Change the decimal to a fraction: 0.123123123.... (1 point)
Answer choices
1 23/100
This decimal is Irrational and cannot be written as a fraction
12 13/10
123/999
123/1000
We can set x = 0.123123123.... and multiply both sides of the equation by 1000 to eliminate the repeating decimals:
1000x = 123.123123123...
Now, we can subtract the two equations to eliminate the repeating decimals:
1000x - x = 123.123123123... - 0.123123123...
999x = 123
To find the fraction form, we divide both sides of the equation by 999:
999x/999 = 123/999
Simplifying the fraction gives:
x = 123/999
Therefore, the decimal 0.123123123.... as a fraction is 123/999.