Change the decimal to a fraction: 0.123123123….(1 point)
Responses
This decimal is Irrational and cannot be written as a fraction
This decimal is Irrational and cannot be written as a fraction
123999
123 over 999
1231000
123 over 1000
123100
1 and 23 over 100
121310
This decimal is Irrational and cannot be written as a fraction
are you sure
Yes, I am sure. The decimal 0.123123123... is a repeating decimal, meaning that the pattern of digits (123) repeats indefinitely. A repeating decimal can be written as a fraction by setting up an equation to solve for the fraction. In this case, let x = 0.123123123...
Then, if we multiply both sides of the equation by 1000, we get 1000x = 123.123123123...
Next, if we subtract the original equation from the equation multiplied by 1000, we get:
1000x - x = 123.123123123... - 0.123123123...
which simplifies to:
999x = 123
Now, we can divide both sides of the equation by 999 to solve for x:
x = 123/999
So, the decimal 0.123123123... can be written as the fraction 123/999, which simplifies to 41/333.