Question

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. \(-2.7\) and \(\frac{3}{4}\)

Short answer

-2.7 < 3/4 and 3/4 > -2.7

Step-by-step solution

Representation of numbers on the number line

To graph the numbers \(-2.7\) and \(\frac{3}{4}\) on a number line, start from zero. Move 2.7 units to the left for \(-2.7\) and a little less than 1 unit to the right for \(\frac{3}{4}\). Make sure to label each number below the point on the line.

Comparing numbers by inspection

From the number line, it can be observed that \(-2.7\) is to the left of zero and \(\frac{3}{4}\) is to the right. Encompassing that \(a < b\) for numbers \(a\) and \(b\) on a number line if \(a\) is to the left of \(b\), it can be deduced that \(-2.7 < \frac{3}{4}\). Reversing the inequality gives \(\frac{3}{4} > -2.7\)