Solve {l}{8.5div10^1}{1.28div10^3}

$$\left. \begin{array} { l } { 8.5 \div 10 ^ { 1 } } \\ { 1.28 \div 10 ^ { 3 } } \end{array} \right.$$

Sort

$$0.00128,0.85$$

Solution Steps

Calculate 10 to the power of 1 and get 10.

$$sort(\frac{8.5}{10},\frac{1.28}{10^{3}})$$

Expand \frac{8.5}{10} by multiplying both numerator and the denominator by 10.

$$sort(\frac{85}{100},\frac{1.28}{10^{3}})$$

Reduce the fraction \frac{85}{100} to lowest terms by extracting and canceling out 5.

$$sort(\frac{17}{20},\frac{1.28}{10^{3}})$$

Calculate 10 to the power of 3 and get 1000.

$$sort(\frac{17}{20},\frac{1.28}{1000})$$

Expand \frac{1.28}{1000} by multiplying both numerator and the denominator by 100.

$$sort(\frac{17}{20},\frac{128}{100000})$$

Reduce the fraction \frac{128}{100000} to lowest terms by extracting and canceling out 32.

$$sort(\frac{17}{20},\frac{4}{3125})$$

Least common denominator of the numbers in the list \frac{17}{20},\frac{4}{3125} is 12500. Convert numbers in the list to fractions with denominator 12500.

$$\frac{10625}{12500},\frac{16}{12500}$$

To sort the list, start from a single element \frac{10625}{12500}.

$$\frac{10625}{12500}$$

Insert \frac{16}{12500} to the appropriate location in the new list.

$$\frac{16}{12500},\frac{10625}{12500}$$

Replace the obtained fractions with the initial values.

$$\frac{4}{3125},\frac{17}{20}$$

Evaluate

$$0.85,\ 0.00128$$