diff --git a/include/fmt/format-inl.h b/include/fmt/format-inl.h
index ed87209e..511c8d85 100644
--- a/include/fmt/format-inl.h
+++ b/include/fmt/format-inl.h
@@ -2246,7 +2246,8 @@ FMT_HEADER_ONLY_CONSTEXPR20 int format_float(Float value, int precision,
       precision = handler.precision;
     }
   } else {
-    exp = static_cast<int>(std::log10(value));
+    // Use floor because 0.9 = 9e-1.
+    exp = static_cast<int>(std::floor(std::log10(value)));
     if (fixed) adjust_precision(precision, exp + 1);
   }
   if (use_dragon) {
diff --git a/include/fmt/format.h b/include/fmt/format.h
index 55cd4409..08c1f7d0 100644
--- a/include/fmt/format.h
+++ b/include/fmt/format.h
@@ -2256,6 +2256,8 @@ FMT_CONSTEXPR20 auto write(OutputIt out, T value,
       throw_format_error("number is too big");
     else
       ++precision;
+  } else if (fspecs.format != float_format::fixed && precision == 0) {
+    precision = 1;
   }
   if (const_check(std::is_same<T, float>())) fspecs.binary32 = true;
   if (!std::numeric_limits<T>::is_iec559 || std::numeric_limits<T>::digits > 64)
diff --git a/test/format-test.cc b/test/format-test.cc
index 72423017..e7b23b7c 100644
--- a/test/format-test.cc
+++ b/test/format-test.cc
@@ -948,6 +948,9 @@ TEST(format_test, precision) {
   EXPECT_THAT(outputs,
               testing::Contains(fmt::format("{:.838A}", -2.14001164E+38)));
 
+  auto ld = 8.43821965335442234493E-4933L;
+  EXPECT_EQ(fmt::format("{:.0}", ld), ld != 0 ? "8e-4933" : "0");
+
   EXPECT_EQ("123.", fmt::format("{:#.0f}", 123.0));
   EXPECT_EQ("1.23", fmt::format("{:.02f}", 1.234));
   EXPECT_EQ("0.001", fmt::format("{:.1g}", 0.001));