diff --git a/python/number.py b/python/number.py
index 3f74235c..aaf238fd 100644
--- a/python/number.py
+++ b/python/number.py
@@ -295,7 +295,8 @@ def __init__(self, data, accuracy=None, precision=None):
             self.accuracy = self.decimal_precision
         else:
             if accuracy is None:
-                accuracy = self.gen.precision()
+                accuracy = prec_bits_to_dec(64 * (self.gen.sizeword() - 2))
+
             self.accuracy = min(accuracy, self.decimal_precision)
         self._parent = SnapPyNumbers(self._precision)
         if _within_sage: