1. **State the problem:** We are given the wavelength of an X-ray as $4.5 \times 10^{-11}$ meters and need to find its wavenumber. 2. **Formula:** The wavenumber $\tilde{\nu}$ is the reciprocal of the wavelength $\lambda$: $$\tilde{\nu} = \frac{1}{\lambda}$$ 3. **Calculate the wavenumber:** $$\tilde{\nu} = \frac{1}{4.5 \times 10^{-11}}$$ 4. **Simplify the expression:** $$\tilde{\nu} = \frac{1}{4.5} \times \frac{1}{10^{-11}} = \frac{1}{4.5} \times 10^{11}$$ 5. **Calculate $\frac{1}{4.5}$:** $$\frac{1}{4.5} = 0.222\overline{2}$$ 6. **Multiply:** $$\tilde{\nu} = 0.222\overline{2} \times 10^{11} = 2.22 \times 10^{10}$$ 7. **Write $8.794 \times 10^{10}$ as a normal number:** Move the decimal 10 places to the right: $$8.794 \times 10^{10} = 879400000000$$ 8. **Write the diameter of DNA helix $2 \times 10^{-9}$ m as a decimal numeral:** Move the decimal 9 places to the left: $$2 \times 10^{-9} = 0.000000002$$ **Final answers:** - Wavenumber of X-ray: $2.22 \times 10^{10}$ m$^{-1}$ - $8.794 \times 10^{10}$ as a normal number: 879400000000 - Diameter of DNA helix as decimal: 0.000000002 m