diff --git a/include/nlohmann/detail/input/lexer.hpp b/include/nlohmann/detail/input/lexer.hpp
index 62d517e86..4c3665593 100644
--- a/include/nlohmann/detail/input/lexer.hpp
+++ b/include/nlohmann/detail/input/lexer.hpp
@@ -1538,7 +1538,10 @@ scan_number_done:
                 position.chars_read_current_line += (len - 1);
                 return integer_result;
             }
-            // the value overflowed: fall through and let the float tail handle it
+            // The value does not fit an integer, so this token converts as a
+            // float. Recording that here keeps convert_number() below from
+            // repeating the integer attempt that just failed.
+            number_type = token_type::value_float;
         }
 #endif
 
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 9ba0445a3..955add0ef 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -9885,7 +9885,10 @@ scan_number_done:
                 position.chars_read_current_line += (len - 1);
                 return integer_result;
             }
-            // the value overflowed: fall through and let the float tail handle it
+            // The value does not fit an integer, so this token converts as a
+            // float. Recording that here keeps convert_number() below from
+            // repeating the integer attempt that just failed.
+            number_type = token_type::value_float;
         }
 #endif