What does it mean to order numbers?

Ordering numbers is an arrangement of the numbers in any sequence. The sequence of the numbers can be in ascending order or descending order.

Ascending order

The ascending order is the arrangement of the numbers or alphabet from smallest values to biggest or greatest. An example of the ascending order is $$2$$, $$5$$, $$9$$, $$15$$, $$32 {\cdots}$$.

Descending order

The descending order is the arrangement of the numbers or alphabet from the greatest or biggest values to the smallest. An example of the descending order is $$Y$$, $$P$$, $$L$$, $$F$$, $$C {\cdots}$$.

E1.5: Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts.

For arranging the numbers in ascending or descending order, all the ordering numbers have to be compared.

An example of ordering numbers is four people are running around a ground, and they covered different distances at the same time as $$\frac{25}{4}\text{ miles}$$, $$\frac{23}{4}\text{ miles }$$, $$\frac{15}{2}\text{ miles }$$, and $$\frac{19}{4}\text{ miles }$$. Order these distances of miles in ascending order.

Worked example

Example 1: Arrange the numbers $$32$$, $$5$$, $$79$$, $$82$$, $$54$$, $$36$$, $$46$$, $$8$$ in the ascending order.

Step 1: Arrange the number in ascending order one by one.

$$5$$ is the smallest among all the numbers. So, $$5$$, $$32$$, $$79$$, $$82$$, $$54$$, $$36$$, $$46$$, $$8$$.

Now, $$8$$ is smaller than all the numbers but greater than $$5$$. So, the arrangement becomes $$5$$, $$8$$, $$32$$, $$79$$, $$82$$, $$54$$, $$36$$, $$46$$.

After this, $$32$$ is greater than $$5$$ and $$8$$. So, the arrangement remains the same.

Now, $$36$$ is greater than $$32$$. So, the arrangement becomes $$5$$, $$8$$, $$32$$, $$36$$, $$79$$, $$82$$, $$54$$, $$46$$.

After that, $$46$$ is greater than $$36$$. So, the arrangement becomes $$5$$, $$8$$, $$32$$, $$36$$, $$46$$, $$79$$, $$82$$, $$54$$.

Now, $$54$$ is greater than $$46$$. So, the arrangement becomes $$5$$, $$8$$, $$32$$, $$36$$, $$46$$, $$54$$, $$79$$, $$82$$.

Then, $$79$$ is greater than $$54$$, and the greatest number is placed last. So, the arrangement remains the same.

Step 2: The final answer after arranging the numbers

The final answer after arranging the numbers is $$5$$, $$8$$, $$32$$, $$36$$, $$46$$, $$54$$, $$79$$, $$82$$.

E1.6: Order quantities by the magnitude and demonstrate familiarity with the symbols

In ordering numbers, if ascending and descending order of the negative numbers has to be arranged, in this, the highest negative number will be the smallest number, and the lowest negative number will be the greatest number. If there are two numbers $$-4$$ and $$-10$$, $$-4$$ is greater than $$-10$$. The numbers that are compared by each other should have the same units. 

An example is the speed of the two cars. Suppose $$45\text{ m}{\setminus} s$$ and $$-48\text{ km}{\setminus} hr$$, in this condition, the units are different, so convert the units and then compare for the highest speed.

Worked example

Example 1: Find the longest and shortest distance among $$25\text{ m}$$, $$56\text{ m}$$, $$42\text{ m}$$, $$-23.4\text{ m}$$, $$89\text{ m}$$, and $$15\text{ m}$$.

Step 1: First, compare the units of each number given.

On comparing the units, all numbers have the same unit. So, the longest and shortest distance can be found easily.

Step 2: Now, find the longest and shortest distance among the given distance.

The largest distance is $$89\text{ m}$$, and the shortest distance is $$-23.4\text{ m}$$.