Final answer:
To rewrite the quantity 5.0 x 10^-7 m using more appropriate units resulting in a number bigger than one but less than one thousand, we convert it to nanometers, resulting in 500 nm. The correct choice from the options provided is therefore 5.0 x 10^-4 mm.
Step-by-step explanation:
To rewrite the quantity 5.0 x 10^-7 m using more appropriate units that result in a number bigger than one but less than 1000, we need to convert the meters into a smaller metric unit. First, we recognize that 1 micrometer (µm) is equal to 1 x 10^-6 m. Therefore, if we convert meters into micrometers for the given quantity:
- 5.0 x 10^-7 m is equivalent to 5.0 x 10^-1 µm (because we are multiplying by 10^6 when converting from meters to micrometers).
- By simplifying 5.0 x 10^-1 µm, we get 0.5 µm, which is less than one.
- To get a numerical value between one and one thousand, we could instead convert to nanometers (nm), where 1 nm = 1 x 10^-9 m.
- Thus, 5.0 x 10^-7 m is equivalent to 500 nm (because we multiply by 10^9 when converting from meters to nanometers).
From the options given, 5.0 x 10^-4 mm is equivalent to 500 nm, which is the correct conversion consistent with the target range of between one and one thousand. By converting the original length to a smaller metric unit, we achieve the requirement for a more appropriate unit of length.