2.1¯¯¯=219
2.
1
¯
=
2
1
9
Showing the work
Let X equal our decimal number (fraction)
Equation 1:
X=2.1¯¯¯(1)
(1) X=2.
1
¯
Since we have 1 digits in our repeating decimal
group, create a second equation by multiplying
both sides by 101 = 10
Equation 2:
10X=21.1¯¯¯(2)
(2) 10X=21.
1
¯
Subtracting equation (1) from (2)
10XX9X===21.1...2.1...19
10X = 21.1... X = 2.1... 9X = 19
We get
9X=19
9
X
=
19
Solving for X
X=199
X
=
19
9
Simplifying the improper fraction,
=219
=
2
1
9
In conclusion,
2.1¯¯¯=219
2.
1
¯
=
2
1/9
