Question

part b true - false
classify each of these statements as always true, at; sometimes true, st; or never true, nt.

1. the units of a conversion factor must cancel.
2. the conversion factor for changing between grams and milligrams is $\frac{1g}{1000mg}$.
3. multiple conversion factors can be used to solve complex conversion problems.
4. if density = mass/volume, then mass = density/volume.
5. when two measurements are equal, a ratio of these two measurements will equal unity.

Explanation:

Step1: Understand conversion - factor concept

In unit - conversion, for the calculation to be correct, the units of a conversion factor must cancel out. For example, when converting from meters to centimeters using the factor $\frac{100\ cm}{1\ m}$, the'm' units cancel. So, statement 11 is always true.

Step2: Check grams - milligrams conversion factor

The correct conversion factor from grams to milligrams is $\frac{1000\ mg}{1\ g}$, not $\frac{1\ g}{1000\ mg}$. So, statement 12 is never true.

Step3: Consider complex conversion problems

In complex unit - conversion problems, multiple conversion factors are often used. For example, converting from miles per hour to meters per second may require conversion of length (miles to meters) and time (hours to seconds) using different conversion factors. So, statement 13 is always true.

Step4: Rearrange density formula

Given density $d=\frac{m}{V}$, by cross - multiplying, we get $m = d\times V$, not $m=\frac{d}{V}$. So, statement 14 is never true.

Step5: Analyze ratio of equal measurements

If two measurements are equal, say $a = b$, then the ratio $\frac{a}{b}=1$ (unity). So, statement 15 is always true.

Answer:

1. AT
2. NT
3. AT
4. NT
5. AT