Question

Which of these nonterminating decimals can be converted into a rational number? (1 point)
0.626226222…
0.020220222…
0.123123123…
0.898998999…

Answer 1

The only one which is a true "repeating" decimal number is
.123123123...
= 123/999
= 41/333

Answer 2

A rational number is a number that can be expressed as the fraction :

p / q

where p and q are two integers

0.123123...

because:

1000 • 0.123123 - 0.123123 = 123.123123... - 0.123123...

999 • 0.123123...= 123

Divide both sides by 999.

0.123123... = 123 / 999 = 3 • 41 / 3 • 333

0.123123... = 41 / 333