diff --git a/equinox/nn/_normalisation.py b/equinox/nn/_normalisation.py
index 9405da7d..54743bf4 100644
--- a/equinox/nn/_normalisation.py
+++ b/equinox/nn/_normalisation.py
@@ -120,7 +120,7 @@ def __call__(
         """**Arguments:**
 
         - `x`: A JAX array, with the same shape as the `shape` passed to `__init__`.
-        - `state`: Ignored; provided for interchangability with the
+        - `state`: Ignored; provided for interchangeability with the
             [`equinox.nn.BatchNorm`][] API.
         - `key`: Ignored; provided for compatibility with the rest of the Equinox API.
             (Keyword only argument.)
@@ -155,9 +155,9 @@ def __call__(
         inv = jax.lax.rsqrt(variance + self.eps)
         out = (x - mean) * inv
         if self.use_weight:
-            out = self.weight * out
+            out = self.weight.astype(dtype) * out  # pyright: ignore
         if self.use_bias:
-            out = out + self.bias
+            out = out + self.bias.astype(dtype)  # pyright: ignore
         if state is sentinel:
             return out.astype(orig_dtype)
         else:
@@ -231,10 +231,6 @@ def __init__(
         self.channels = channels
         self.eps = eps
         self.channelwise_affine = channelwise_affine
-
-        with jax.numpy_dtype_promotion("standard"):
-            dtype = jnp.result_type(dtype, jnp.float32)
-
         self.weight = jnp.ones(channels, dtype=dtype) if channelwise_affine else None
         self.bias = jnp.zeros(channels, dtype=dtype) if channelwise_affine else None
 
@@ -283,7 +279,7 @@ def __call__(
         if self.channelwise_affine:
             weight = left_broadcast_to(self.weight, out.shape)  # pyright: ignore
             bias = left_broadcast_to(self.bias, out.shape)  # pyright: ignore
-            out = weight * out + bias
+            out = weight.astype(dtype) * out + bias.astype(dtype)
         if state is sentinel:
             return out.astype(orig_dtype)
         else:
@@ -354,10 +350,6 @@ def __init__(
         self.eps = eps
         self.use_weight = use_weight
         self.use_bias = use_bias
-
-        with jax.numpy_dtype_promotion("standard"):
-            dtype = jnp.result_type(dtype, jnp.float32)
-
         self.weight = jnp.ones(shape, dtype=dtype) if use_weight else None
         self.bias = jnp.zeros(shape, dtype=dtype) if use_bias else None
 
@@ -410,9 +402,9 @@ def __call__(
         out = inv_rms * x
 
         if self.use_weight:
-            out = self.weight * out
+            out = self.weight.astype(dtype) * out  # pyright: ignore
         if self.use_bias:
-            out = out + self.bias
+            out = out + self.bias.astype(dtype)  # pyright: ignore
         if state is sentinel:
             return out.astype(orig_dtype)
         else: