diff --git a/include/fmt/format-inl.h b/include/fmt/format-inl.h
index 80e0f8f4..5ebad700 100644
--- a/include/fmt/format-inl.h
+++ b/include/fmt/format-inl.h
@@ -1626,7 +1626,8 @@ struct fixed_handler {
     }
     if (buf[0] > '9') {
       buf[0] = '1';
-      buf[size++] = '0';
+      if (fixed) buf[size++] = '0';
+      else ++exp10;
     }
     return digits::done;
   }
@@ -2466,7 +2467,7 @@ int format_float(T value, int precision, float_specs specs, buffer<char>& buf) {
     exp += handler.size - cached_exp10 - 1;
     fallback_format(value, handler.precision, specs.binary32, buf, exp);
   } else {
-    exp -= cached_exp10;
+    exp += handler.exp10;
     buf.try_resize(to_unsigned(handler.size));
   }
   if (!fixed && !specs.showpoint) {
diff --git a/test/format-test.cc b/test/format-test.cc
index 911d1d58..d5d3f6c9 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -957,6 +957,7 @@ TEST(FormatterTest, Precision) {
   EXPECT_EQ("0.001", format("{:.1g}", 0.001));
   EXPECT_EQ("1019666400", format("{}", 1019666432.0f));
   EXPECT_EQ("1e+01", format("{:.0e}", 9.5));
+  EXPECT_EQ("1.0e-34", fmt::format("{:.1e}", 1e-34));
 
   EXPECT_THROW_MSG(format("{0:.2}", reinterpret_cast<void*>(0xcafe)),
                    format_error,