The intensity of the \oiv~2s$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ 2p $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$P-2s2p$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$P and \siv~3 s$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ 3p $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$P- 3s 3p$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ $\mathrm{<mrow\; data-mjx-texclass="ORD">4</mrow>}$ P intercombination lines around 1400~\AA~observed with the \textit{Interface Region Imaging Spectrograph} (IRIS) provide a useful tool to diagnose the electron number density ($Ne$) in the solar transition region plasma. We measure the electron number density in a variety of solar features observed by IRIS, including an active region (AR) loop, plage and brightening, and the ribbon of the 22-June-2015 M 6.5 class flare. By using the emissivity ratios of \oiv\ and \siv\ lines, we find that our observations are consistent with the emitting plasma being near isothermal (log$T$[K] $\approx$ 5) and iso-density ($Ne$ $\approx$~10$\mathrm{<mrow\; data-mjx-texclass="ORD">10.6</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$) in the AR loop. Moreover, high electron number densities ($Ne$ $\approx$~10$\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$) are obtained during the impulsive phase of the flare by using the \siv\ line ratio. We note that the \siv\ lines provide a higher range of density sensitivity than the \oiv\ lines. Finally, we investigate the effects of high densities ($Ne$ $\gtrsim$ 10$\mathrm{<mrow\; data-mjx-texclass="ORD">11</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$) on the ionization balance. In particular, the fractional ion abundances are found to be shifted towards lower temperatures for high densities compared to the low density case. We also explored the effects of a non-Maxwellian electron distribution on our diagnostic method.