classify each of these statements as always true, sometimes true, or never true.
__ST___11)The unit of a conversion factor must cancel.
__AT___12)the conversion factor for changing grams and milligrams is 1g/1000mg
___ST__13)multiple conversions factors can be used to solve complex conversion problems.
___NT____14)if density=mass/volume, then mass= density/volume.
____NT_____15)when two measurements are equal, a ratio of these two measurements will equal unity.
14 is ok.
15 is not. If two measurements are equal, for example one measurement is 14 and the other is 14, then 14/14 = 1, nicht wahr?
11. Confusing to me. I don't know that they MUST cancel. It depends upon what is being done.
12. Again I am confused. As it is written with grams AND milligrams, the factor 1g/1000 mg is ok but it might be the inverted form in some cases.
The factor IS 1/1000
13. I tend to think multiple conversion factors will always work if we can find the factors.
I hope this helps a little.
To classify each statement as always true, sometimes true, or never true, let's analyze them one by one:
11) The unit of a conversion factor must cancel.
This statement is sometimes true. In most cases, the units in the conversion factor should cancel out, meaning that they should have opposite units. For example, if you're converting meters to kilometers, the conversion factor would be 1 km/1000 m, where the units "km" and "m" cancel each other out. However, there may be certain situations where the conversion factor does not involve unit cancellation, such as when converting between two equivalent units, like Celsius and Kelvin.
12) The conversion factor for changing grams and milligrams is 1g/1000mg.
This statement is always true. The conversion factor between grams and milligrams is indeed 1g/1000mg. This means that to convert from grams to milligrams, you would multiply the given value by 1, and to convert from milligrams to grams, you would divide the given value by 1000.
13) Multiple conversion factors can be used to solve complex conversion problems.
This statement is always true. Complex conversion problems often require the use of multiple conversion factors. By using multiple conversion factors, you can convert from one unit to another by canceling out the units step by step, until you reach the desired unit. This allows for more flexibility in solving complex conversion problems.
14) If density = mass/volume, then mass = density/volume.
This statement is always true. The given equation is correct - density is defined as the mass divided by the volume. Therefore, rearranging the equation, you can solve for mass by multiplying both sides of the equation by volume: mass = density * volume.
15) When two measurements are equal, a ratio of these two measurements will equal unity.
This statement is never true. If two measurements are equal, the ratio of these measurements will be 1, not necessarily unity. For example, if you have a measurement of 5 meters and another measurement of 5 meters, the ratio of these two measurements would be 5/5 = 1, not necessarily "unity." Unity refers to the numerical value of 1.
Hope this explanation clarifies the classification of each statement for you.