diff --git a/include/nlohmann/detail/output/binary_writer.hpp b/include/nlohmann/detail/output/binary_writer.hpp
index efc5c5331d..aff4093c5d 100644
--- a/include/nlohmann/detail/output/binary_writer.hpp
+++ b/include/nlohmann/detail/output/binary_writer.hpp
@@ -177,7 +177,8 @@ class binary_writer
 
             case value_t::number_float:
             {
-		double valueD = j.m_value.number_float;
+		const auto valueD = j.m_value.number_float;
+		const float valueF = static_cast<float>(valueD);
 		if (std::isnan(valueD)) {
 		    // NaN is 0xf97e00 in CBOR
 		    oa->write_character(to_char_type(0xF9));
@@ -189,8 +190,13 @@ class binary_writer
 		    oa->write_character(valueD > 0 ? to_char_type(0x7C) : to_char_type(0xFC));
 		    oa->write_character(to_char_type(0x00));
 		} else {
-		    oa->write_character(get_cbor_float_prefix(valueD));
-		    write_number(valueD);
+                    if(static_cast<double>(valueF) == valueD) {
+		        oa->write_character(get_cbor_float_prefix(valueF));
+		        write_number(valueF);
+                    } else {
+		        oa->write_character(get_cbor_float_prefix(valueD));
+		        write_number(valueD);
+                    }
 		}
                 break;
             }
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index ac44a99dd5..89e05a8116 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -12164,7 +12164,8 @@ class binary_writer
 
             case value_t::number_float:
             {
-		double valueD = j.m_value.number_float;
+		const auto valueD = j.m_value.number_float;
+		const float valueF = static_cast<float>(valueD);
 		if (std::isnan(valueD)) {
 		    // NaN is 0xf97e00 in CBOR
 		    oa->write_character(to_char_type(0xF9));
@@ -12176,8 +12177,13 @@ class binary_writer
 		    oa->write_character(valueD > 0 ? to_char_type(0x7C) : to_char_type(0xFC));
 		    oa->write_character(to_char_type(0x00));
 		} else {
-		    oa->write_character(get_cbor_float_prefix(valueD));
-		    write_number(valueD);
+                    if(static_cast<double>(valueF) == valueD) {
+		        oa->write_character(get_cbor_float_prefix(valueF));
+		        write_number(valueF);
+                    } else {
+		        oa->write_character(get_cbor_float_prefix(valueD));
+		        write_number(valueD);
+                    }
 		}
                 break;
             }
diff --git a/test/src/unit-cbor.cpp b/test/src/unit-cbor.cpp
index c49899bb00..b9ee8bce5c 100644
--- a/test/src/unit-cbor.cpp
+++ b/test/src/unit-cbor.cpp
@@ -853,6 +853,20 @@ TEST_CASE("CBOR")
 
                     CHECK(json::from_cbor(result, true, false) == j);
                 }
+                SECTION("0.5")
+                {
+                    double v = 0.5;
+                    json j = v;
+                    // its double-precision float binary value is
+                    // {0xfb, 0x3f, 0xe0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}
+                    // but to save memory, we can store it as single-precision float.
+                    std::vector<uint8_t> expected = {0xfa, 0x3f, 0x00, 0x00, 0x00};
+                    const auto result = json::to_cbor(j);
+                    CHECK(result == expected);
+                    // roundtrip
+                    CHECK(json::from_cbor(result) == j);
+                    CHECK(json::from_cbor(result) == v);
+                }
             }
 
             SECTION("half-precision float (edge cases)")