Question

make 12 cards in which different rational numbers are written arrange the cards in ascending or descending order of rational number by converting them into decimals. for example :<br />2/3,-1/2,0,3/2,4/3,5,-8,5/2,-23,213,-15/3,7/2 are one set of 12 such rational numbers please answer it urgent send please

Answer 1

first ascending- -23,-8,-15/3,-8/3,-1/2,0,2,3,5,2/3,2/4,5/7/2,213
descending order- 213,7/2,5,4,3/2,5/2,3,2,0,-1/2,-8/3,-15/3,-8,-23

Answer 2

Answer:

The order is $213 > \frac{7}{2} > \frac{5}{2} > \frac{3}{2} > \frac{4}{3} > \frac{2}{3} > 0 > -\frac{1}{2} > -\frac{15}{3} > -8 > -23.$

Step-by-step explanation:

To determine: The ascending and descending order of the given rational numbers

Given: $\frac{2}{3}, -\frac{1}{2}, 0, \frac{3}{2}, \frac{4}{3}, 5, -8, \frac{5}{2}, -23, 213, -\frac{15}{3}, \frac{7/2}$

Step 1: Convert each rational number into decimals

                $\frac{2}{3} = 0.66\\-\frac{1}{2} = -0.5\\0 = 0\\\frac{3}{2} = 1.5\\\frac{4}{3} = 1.33\\5 = 5\\-8 = -8\\\frac{5}{2} = 2.5\\-23 = -23\\213 = 213\\-\frac{15}{3} = -5\\\frac{7}{2} = 3.5$

Step 2: The decimals that have the negative sign will be less than 0 and those with positive will be greater than 0. Let us group the negative decimals together (not in any order) and place them as being less than 0 and the positive decimals together and place them greater than 0

           $[-0. 5, -8, -23, -5] < 0 < [0.66, 1.5, 1.33, 2.5, 213, 3.5]$

Step 3: Positive numbers are placed in ascending order based on the value to the left of decimal point. If both the numbers are same then the number after the decimal point is considered and checked for which is greater or lesser and this goes on  

So, we can order the positive decimals as follows

 

                 $[-0.5, -8, -23, -5] < 0 < 0.66 < 1.33 < 1.5 < 2.5 < 3.5 < 213$

Step 4: In negative decimals, it is the reverse case, the higher the magnitude the lower is its value. So, for example while comparing -5 and                              -23

                                             -5> -23

So, we can order the negative decimals as follows

                                    -23 < -8 < -5 < -0.5

Thus, the decimals in ascending order is

         -23 < -8 < -5 < -0.5 < 0 < 0.66 < 1.33 < 1.5 < 2.5 < 3.5 < 213

The equivalent rational numbers in same order is

                    -$23 < -8 < -\frac{15}{3} <-\frac{1}{2} < 0 < \frac{2}{3} < \frac{4}{3} < \frac{3}{2} < \frac{5}{2} < \frac{7}{2} < 213$

Thus, the decimals in descending order is

                     213 > 3.5 > 2.5 > 1.5 > 1.33 > 0.66 > 0 > -0.5 > -5 > -8 > -23

The equivalent rational numbers in same order is

                  $213 > \frac{7}{2} > \frac{5}{2} > \frac{3}{2} > \frac{4}{3} > \frac{2}{3} > 0 > -\frac{1}{2} > -\frac{15}{3} > -8 > -23.$