Question

Perform each of the following conversions. a. \(8.43 \mathrm{~cm}\) to millimeters b. \(2.41 \times 10^{2} \mathrm{~cm}\) to meters c. \(294.5 \mathrm{~nm}\) to centimeters d. \(1.445 \times 10^{4} \mathrm{~m}\) to kilometers e. \(235.3 \mathrm{~m}\) to millimeters f. \(903.3 \mathrm{~nm}\) to micrometers

Short answer

a. \(84.3 \mathrm{~mm}\) b. \(2.41 \mathrm{~m}\) c. \(2.945 \times 10^{-5} \mathrm{~cm}\) d. \(14.45 \mathrm{~km}\) e. \(235300 \mathrm{~mm}\) f. \(0.9033 \mathrm{~\mu m}\)

Step-by-step solution

(Conversion 1: Centimeters to Millimeters)

We have 8.43 cm and we need to convert it to millimeters. We know that 1 cm = 10 mm. Therefore, we multiply the given value by 10: \(8.43 \mathrm{~cm} \times 10 = 84.3 \mathrm{~mm}\)

(Conversion 2: Centimeters to Meters)

We have \(2.41 \times 10^2\) cm and need to convert it to meters. We know that 1 m = 100 cm. Therefore, we divide the given value by 100: \(\frac{2.41 \times 10^2 \mathrm{~cm}}{100} = 2.41 \mathrm{~m}\)

(Conversion 3: Nanometers to Centimeters)

We have 294.5 nm and need to convert it to centimeters. We know that 1 nm = \(10^{-9}\) m and 1 m = 100 cm. Therefore, we first convert nm to m and then m to cm: \(294.5 \mathrm{~nm} \times 10^{-9} \mathrm{~m/nm} = 2.945 \times 10^{-7} \mathrm{~m}\) \(2.945 \times 10^{-7} \mathrm{~m} \times 100 \mathrm{~cm/m} = 2.945 \times 10^{-5} \mathrm{~cm}\)

(Conversion 4: Meters to Kilometers)

We have \(1.445 \times 10^4\) m and need to convert it to kilometers. We know that 1 km = 1000 m. Therefore, we divide the given value by 1000: \(\frac{1.445 \times 10^4 \mathrm{~m}}{1000} = 14.45 \mathrm{~km}\)

(Conversion 5: Meters to Millimeters)

We have 235.3 m and need to convert it to millimeters. We know that 1 m = 1000 mm. Therefore, we multiply the given value by 1000: \(235.3 \mathrm{~m} \times 1000 = 235300 \mathrm{~mm}\)

(Conversion 6: Nanometers to Micrometers)

We have 903.3 nm and need to convert it to micrometers. We know that 1 nm = \(10^{-9}\) m and 1 μm = \(10^{-6}\) m. Therefore, we first convert nm to m and then m to μm: \(903.3 \mathrm{~nm} \times 10^{-9} \mathrm{~m/nm} = 9.033 \times 10^{-7} \mathrm{~m}\) \(9.033 \times 10^{-7} \mathrm{~m} \times \frac{1 \times 10^{6} \mathrm{~\mu m}}{1 \mathrm{~m}} = 0.9033 \mathrm{~\mu m} \)