Solve {l}{0.111111}{1/5}{1/7}

$$\left. \begin{array} { l } { 0.111111 } \\ { \frac { 1 } { 5 } } \\ { \frac { 1 } { 7 } } \end{array} \right.$$

Sort

$$0.111111,\frac{1}{7},0.2$$

Solution Steps

Convert decimal numbers in the list 0.111111,\frac{1}{5},\frac{1}{7} to fractions.

$$\frac{111111}{1000000},\frac{1}{5},\frac{1}{7}$$

Least common denominator of the numbers in the list \frac{111111}{1000000},\frac{1}{5},\frac{1}{7} is 7000000. Convert numbers in the list to fractions with denominator 7000000.

$$\frac{777777}{7000000},\frac{1400000}{7000000},\frac{1000000}{7000000}$$

To sort the list, start from a single element \frac{777777}{7000000}.

$$\frac{777777}{7000000}$$

Insert \frac{1400000}{7000000} to the appropriate location in the new list.

$$\frac{777777}{7000000},\frac{1400000}{7000000}$$

Insert \frac{1000000}{7000000} to the appropriate location in the new list.

$$\frac{777777}{7000000},\frac{1000000}{7000000},\frac{1400000}{7000000}$$

Replace the obtained fractions with the initial values.

$$0.111111,\frac{1}{7},\frac{1}{5}$$

Evaluate

$$0.111111,\ 0.2,\ \frac{1}{7}$$