Question

Different sizes of ribbon need to be cut to go around various shapes for a craft project.

All of the following sizes are in inches. Put the ribbon sizes in order from least to greatest in the blanks below

Answer 1

You have five numbers
`√(6),\ 2(1)/(2),\ -√(1),\ (7)/(2), \ 3.\overline{3}.`

Among them there is one negative number
`-√(1),` this number is smallest.

Note that

`(√(6) )^2=6 \text{ and } \left(2(1)/(2)\right)^2=(2.5)^2=6.25.`

Since 6.25>6, then

`2(1)/(2)>√(6)`

and these numbers are less than 3

Note that

`(7)/(2)=3.5 \text{ and } 3.\overline{3}=3.333333....,`

then
`3.3333333...<3.5` and these numbers are greater than 3.

Therefore, the correct order from the smallest to the greatest is:

`-√(1), \quad √(6),\quad 2(1)/(2),\quad 3.\overline{3}, \quad (7)/(2).`