Question

youre conducting a science experiment measuring temperature changes in four different solutions.
the temperatures changed as follows:

• one solution cooled by $4\frac{3}{4}$ degrees,
• another cooled by 5.6 degrees.
• a third cooled by $3\frac{1}{2}$ degrees.
• and the fourth warmed by 0.45 degrees.

if the numbers $-4\frac{3}{4}$, -5.6, $-3\frac{1}{2}$, and 0.45 represent the temperature changes,
which of the following puts these numbers in order from least to greatest?
select one of four
0.45, $-3\frac{1}{2}$, $-4\frac{3}{4}$, -5.6
0.45, -5.6, $-4\frac{3}{4}$, $-3\frac{1}{2}$
-5.6, $-4\frac{3}{4}$, $-3\frac{1}{2}$, 0.45
$-3\frac{1}{2}$, $-4\frac{3}{4}$, -5.6, 0.45
remaining attempts: 1

Explanation:

Step1: Convert mixed numbers to decimals

First, convert \(-4\frac{3}{4}\) to decimal: \(4\frac{3}{4}=4 + \frac{3}{4}=4 + 0.75 = 4.75\), so \(-4\frac{3}{4}=-4.75\).
Then, convert \(-3\frac{1}{2}\) to decimal: \(3\frac{1}{2}=3 + \frac{1}{2}=3 + 0.5 = 3.5\), so \(-3\frac{1}{2}=-3.5\).

Step2: Compare negative numbers

For negative numbers, the larger the absolute value, the smaller the number.
\(\vert -5.6\vert = 5.6\), \(\vert -4.75\vert = 4.75\), \(\vert -3.5\vert = 3.5\).
Since \(5.6>4.75>3.5\), we have \(-5.6 < -4.75 < -3.5\) (i.e., \(-5.6 < -4\frac{3}{4} < -3\frac{1}{2}\)).

Step3: Compare with positive number

Positive numbers are greater than negative numbers, so \(0.45\) is greater than all negative numbers.

Answer:

\(-5.6, -4\frac{3}{4}, -3\frac{1}{2}, 0.45\)