Question

Graph the numbers on a number line. Then write two inequalities that compare the two numbers. $$-4.1 \text { and }-4.02$$

Short answer

\(-4.1 < -4.02\) and \(-4.02 > -4.1\). The number -4.02 is on the right of -4.1 when represented on the number line because it is greater than -4.1.

Step-by-step solution

Plot the numbers on the number line

The number line begins from negative infinity and goes up till positive infinity. Each point on this line represents a specific real number. Ensure you use appropriate scale for the line, so -4.1 and -4.02 are clearly visible and distinguish area. Note that -4.02 is closer to 0 than -4.1. Therefore, it should be to the right of -4.1 on the number line. Do not forget marking the numbers at the particular points in the line.

Write the first inequality

In the order of the number line, -4.02 is greater than -4.1. This relationship can be expressed with the inequality: \(-4.1 < -4.02\). When reading this inequality from the left, it would be stated, negative 4.1 is less than negative 4.02.

Write the second inequality

Alternatively, the relationship between these two numbers could also be expressed the other way around. This time though, it would be read from the right side of the inequality, giving us \(-4.02 > -4.1\), which would translate to negative 4.02 is greater than negative 4.1.

Review the results

Review the results and validate them against the initial conditions. If all the conditions are met, the problem is solved effectively.