To determine the point that is [tex]\(\frac{1}{4}\)[/tex] of the way from the point 0 to the point -3 on the number line, we need to follow a few steps:
1. Find the distance between the points 0 and -3:
The distance from 0 to -3 on the number line is:
[tex]\[
-3 - 0 = -3
\][/tex]
2. Calculate [tex]\(\frac{1}{4}\)[/tex] of this distance:
We need to find [tex]\(\frac{1}{4}\)[/tex] of the distance found in the first step:
[tex]\[
\frac{1}{4} \times -3 = -0.75
\][/tex]
3. Locate this point on the number line starting from 0:
Starting from the point 0 and moving [tex]\(-0.75\)[/tex] units towards -3, we arrive at:
[tex]\[
0 + (-0.75) = -0.75
\][/tex]
Therefore, the point that is [tex]\(\frac{1}{4}\)[/tex] of the way from 0 to -3 on the number line is [tex]\(\boxed{-0.75}\)[/tex].
