Question

which of the following number lines correctly displays the points below?
{ - 2.25, - 2\frac{2}{5}, - 1.35, - \frac{3}{4} }

Explanation:

Step1: Convert mixed number and fraction to decimal

• Convert \(-2\frac{2}{5}\) to decimal: \(-2\frac{2}{5}=-(2 + \frac{2}{5})=-(2+0.4)=-2.4\)
• Convert \(-\frac{3}{4}\) to decimal: \(-\frac{3}{4}=- 0.75\)

Step2: Compare the values

• We have the values \(-2.4\), \(-2.25\), \(-1.35\), \(-0.75\)
• On a number - line, numbers increase from left to right. So the order from left to right is \(-2.4<-2.25<-1.35<-0.75\)

Step3: Analyze each number - line option

• For the first option: The order of points from left to right is \(-2\frac{2}{5}=-2.4\), \(-2.25\), \(-1.35\), \(-\frac{3}{4}=-0.75\). But looking at the scale: \(-2.6\) to \(-2.2\) (for \(-2\frac{2}{5}=-2.4\) and \(-2.25\)) and \(-1.4\) to \(-0.6\) (for \(-1.35\) and \(-\frac{3}{4}=-0.75\)) is correct in terms of relative positions.
• For the second option: The position of \(-2\frac{2}{5}=-2.4\) is too far to the left compared to the scale (it should be between \(-2.6\) and \(-2.2\) but the spacing is wrong in terms of the given scale for the number - line).
• For the third option: The position of \(-\frac{3}{4}=-0.75\) is not in the correct sub - interval (it should be in the \(-1.0\) to \(-0.6\) sub - interval but the dot is misplaced).
• For the fourth option: The position of \(-2\frac{2}{5}=-2.4\) is too far to the left compared to the scale (it should be between \(-2.6\) and \(-2.2\) but the spacing is wrong in terms of the given scale for the number - line).

Answer:

The first number - line (the one with the first circle option) correctly displays the points.