100 picometer \(=\ldots \ldots \ldots \ldots\) (a) \(10^{-8} \mathrm{~cm}\) (b) \(10^{-7} \mathrm{~m}\) (c) \(10 \times 10^{-6} \mu \mathrm{m}\) (d) \(10 \times 10^{-8} \mu \mathrm{m}\)

First, let's establish the unit conversion factors for length: 1 meter (m) = 100 centimeters (cm) 1 meter (m) = 1,000,000,000,000 picometers (pm) 1 meter (m) = 1,000,000 micrometers (µm)

To convert 100 pm to centimeters, we'll use the conversion factors above: 100 pm × (1 meter / 1,000,000,000,000 pm) × (100 cm / 1 meter) Now, cancel out the meters and picometers, then multiply the remaining numbers: (100 × 100) / 1,000,000,000,000 cm = 10,000 / 1,000,000,000,000 cm = 10^-8 cm

To convert 100 pm to meters, we'll use the conversion factors above: 100 pm × (1 meter / 1,000,000,000,000 pm) Now, cancel out the picometers, then multiply the remaining numbers: 100 / 1,000,000,000,000 m = 10^-10 m

To convert 100 pm to micrometers, we'll use the conversion factors above: 100 pm × (1 meter / 1,000,000,000,000 pm) × (1,000,000 µm / 1 meter) Now, cancel out the meters and picometers, then multiply the remaining numbers: (100 × 1,000,000) / 1,000,000,000,000 µm = 100,000,000 / 1,000,000,000,000 µm = 10^-4 µm = 0.0001 µm Now let's compare our conversions with the given options: (a) 10^-8 cm → This option matches our conversion in Step 2. (b) 10^-7 m → This option does not match our conversion in Step 3. (c) 10 x 10^-6 µm → This option does not match our conversion in Step 4. (d) 10 x 10^-8 µm → This option is not correct, as our conversion in Step 4 gave a different value. Therefore, the correct answer is (a) 100 picometers = 10^-8 cm.