Change the decimal to a fraction: 0.123123123….(1 point) Responses 123100 1 and 23 over 100 121310 12 and 13 tenths 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
To change the decimal 0.123123123… into a fraction, we can call this decimal as x and subtract it from itself shifted by three decimal places, which gives 1000x. This way, the repeating block of digits will be cancelled out.
0.123123123…
- 0.001x (shifted by three decimal places)
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0.122122122...
Now we subtract these two equations:
x - 0.001x = 0.123123123... - 0.122122122...
0.999x = 0.001001001...
Next, we simplify this equation. Since there are three repeating digits after the decimal point, we multiply both sides by 1000:
999x = 1.001001001...
x = 1.001001001... / 999
Therefore, the decimal 0.123123123… can be written as a fraction: 1.001001001... / 999.