diff --git a/docs/guides/specify-observables-pauli.ipynb b/docs/guides/specify-observables-pauli.ipynb
index d65aefa5415..440a0b3c5e8 100644
--- a/docs/guides/specify-observables-pauli.ipynb
+++ b/docs/guides/specify-observables-pauli.ipynb
@@ -147,10 +147,13 @@
     "We expand the observable $O$ as\n",
     "\n",
     "$$\n",
-    "O = \\sum_{P \\in \\{I, X, Y, Z\\}^{\\otimes n}} \\mathrm{Tr}(O P) P,\n",
+    "O =\n",
+    "\\frac{1}{2^n}\n",
+    "\\sum_{P \\in \\{I, X, Y, Z\\}^{\\otimes n}}\n",
+    "\\mathrm{Tr}(O P) P,\n",
     "$$\n",
     "\n",
-    "where the sum runs over all possible $n$-qubit Pauli terms and $\\mathrm{Tr}(\\cdot)$ is the trace of a matrix, which acts as inner product.\n",
+    "where the sum runs over all possible $n$-qubit Pauli terms and $\\mathrm{Tr}(\\cdot)$ is the trace of a matrix, which acts as an inner product. The factor $1/2^n$ accounts for the Hilbert--Schmidt normalization of $n$-qubit Pauli strings.\n",
     "You can implement this decomposition  from a matrix to Pauli terms using the `SparsePauliOp.from_operator` method, like so:"
    ]
   },