Question

a student measured the temperatures (in degrees celsius) of two different chemical mixtures for his science fair project. the temperatures for the mixtures are shown on the number line.
(a) find the absolute value of the temperature for each mixture.
mixture a: \\(|-3| = \square\\)
mixture b: \\(|1| = \square\\)
(b) which mixture’s temperature is closer to zero?
\\(\bigcirc\\) mixture a
\\(\bigcirc\\) mixture b
\\(\bigcirc\\) neither is closer to zero.

Explanation:

Step1: Calculate absolute value of -3

The absolute value of a number \( x \) is \( |x|=

$$\begin{cases}x, & x\geq0\\-x, & x < 0\end{cases}$$

\). For \( x=- 3\), since \(-3<0\), \(|-3|=-(-3) = 3\).

Step2: Calculate absolute value of 1

For \( x = 1\), since \(1\geq0\), \(|1|=1\).

Step3: Compare distances to zero

The absolute value of a number represents its distance from zero on the number line. The distance of Mixture A's temperature (\(-3\)) from zero is \(|-3| = 3\), and the distance of Mixture B's temperature (\(1\)) from zero is \(|1|=1\). Since \(1<3\), Mixture B's temperature is closer to zero.

Answer:

(a) Mixture A: \(3\), Mixture B: \(1\)
(b) Mixture B