  We present a new determination of the distance to M101, host of the type Ia
SN 2011fe, based on the tip of the red giant branch method (TRGB). Our
determination is based on {\it Hubble Space Telescope} archival $F555W$ and
$F814W$ images of nine fields within the galaxy. Color-magnitude diagrams of
arm-free regions in all fields show a prominent red giant branch (RGB). We
measure the $I$-band magnitudes of the TRGB, obtaining a mean value of $I_{\rm
TRGB}=25.28\pm0.01$ (where the error is a standard error), using an
edge-detection method. We derive a weighted mean value of distance modulus
$(m-M)_0=29.30\pm0.01 ({\rm random})\pm0.12 ({\rm systematic})$, corresponding
to a linear distance of $7.24\pm0.03\pm0.40 $ Mpc. While previous estimates for
M101 show a large range (TRGB distances of $(m-M)_0=29.05$ to 29.42 and Cepheid
distances of $(m-M)_0=29.04$ to 29.71), our measurements of the TRGB distances
for nine fields show a small dispersion of only 0.02. We combine our distance
estimate and photometry in the literature to derive absolute peak magnitudes in
optical and near-infrared bands of SN 2011fe. Absolute maximum magnitudes of SN
2011fe are $\sim0.2$ mag brighter in the optical band and much more in the NIR
than the current calibrations of SNe Ia in the literature. From the optical
maximum magnitudes of SN 2011fe we obtain a value of the Hubble constant,
$H_0=65.0\pm0.5({\rm random})\pm5.7({\rm systematic})$ \kmsMpc, slightly
smaller than other recent determinations of $H_0$.
