What if we could combine the $"$ mm $"$ number line and the $"$ km $"$ number line? Could we get the best of both worlds? Could we place more objects on this combined line than on the previous lines?

What value should be placed half way in between these values?

What if we convert both units to meters?

Discuss with your partner question $7.$ Record what factors played a role in your decision in your notebook.

$8.$ What if we equally divide the line into two sections?

How many divisions would you place on the right side? How "big" is each division increment?

How many divisions would you place on the left side? How "big" is each division increment?

$0\mathrm{.}001$ m

Are the left and right side increments the same? So$,$ then can we put the two halves together? Why or why not?

$9.$ Due to the fact that our standard number line doesn't allow us to put the two scales together, we need to determine a new type of number line. On the following page, you will find a new type of number line called a logarithmic number line. Each increment goes up by a multiple of $10$ which is called a maqnitude. This means that any sub division between marks do not have the same value. The first line has been done for you in terms of meters. Complete each of the other lines according to the units listed. $($Hint$!!$ Look for patterns in what you do$!)$