Interpret real numbers in context

Detailed Explanation: Interpret real numbers in context

A real number describes a quantity in a situation. Its meaning depends on the unit, the zero point, and the chosen direction:

• A positive number means a position or amount in the positive direction.
• A negative number means a position or amount in the opposite direction.
• Zero means the reference point or no change.

Worked example

A robot moves along a straight path. Its starting point is $0$ meters. The positive direction is east, and the negative direction is west.

At three different times, the robot is at these positions:

Interpret the positions and put them in order from west to east.

Step 1: Identify what zero means.

The value $(0\text{ m})$ means the robot is exactly at its starting point.

Step 2: Interpret the signs.

The position $(-2.5\text{ m})$ means the robot is $(2.5)$ meters west of the starting point.

The position $\sqrt{2}\text{ m}$ is positive, so the robot is east of the starting point. Since

it is about $(1.414)$ meters east.

Step 3: Place the values on a number line.

Moving from west to east means moving from least to greatest:

Therefore,

Step 4: Interpret the types of numbers.

• $(-2.5)$ is rational because it can be written as a fraction:

Its decimal is exact.

• $0$ is rational because $(0=\frac{0}{1})$.

• $\sqrt{2}$ is irrational. Its decimal goes on forever without repeating. The value $(1.414\ldots)$ is only an approximation, while $\sqrt{2}$ is the exact value.

When interpreting real numbers, always include the units, explain what the sign means, and use a number line or comparison symbols to determine order.