diff --git a/poincare/src/multiplication.cpp b/poincare/src/multiplication.cpp
index afc80acba..39452e2e8 100644
--- a/poincare/src/multiplication.cpp
+++ b/poincare/src/multiplication.cpp
@@ -510,36 +510,44 @@ Expression Multiplication::shallowBeautify(ExpressionNode::ReductionContext redu
       result = units;
     } else {
       double value = result.approximateToScalar<double>(reductionContext.context(), reductionContext.complexFormat(), reductionContext.angleUnit());
-      if (std::isinf(value)) {
-        result = Infinity::Builder(false); //FIXME sign?
-      } else if (std::isnan(value)) {
+      if (std::isnan(value)) {
+        // If the value is undefined, return "undef" without any unit
         result = Undefined::Builder();
       } else {
-        // Identify the first Unit factor and its exponent
-        Expression firstFactor = units;
-        int exponent = 1;
-        if (firstFactor.type() == ExpressionNode::Type::Multiplication) {
-          firstFactor = firstFactor.childAtIndex(0);
-        }
-        if (firstFactor.type() == ExpressionNode::Type::Power) {
-          Expression exp = firstFactor.childAtIndex(1);
-          firstFactor = firstFactor.childAtIndex(0);
-          assert(exp.type() == ExpressionNode::Type::Rational && static_cast<Rational &>(exp).isInteger());
-          Integer expInt = static_cast<Rational &>(exp).signedIntegerNumerator();
-          if (expInt.isLowerThan(Integer(Integer::k_maxExtractableInteger))) {
-            exponent = expInt.extractedInt();
-          } else {
-            // The exponent is too large to be extracted, so do not try to use it.
-            exponent = 0;
+        Expression resultWithoutUnit;
+        if (std::isinf(value)) {
+          resultWithoutUnit = Infinity::Builder(value < 0.0);
+        } else {
+          // Find the right unit prefix when the value ≠ 0
+          if (value != 0.0) {
+            // Identify the first Unit factor and its exponent
+            Expression firstFactor = units;
+            int exponent = 1;
+            if (firstFactor.type() == ExpressionNode::Type::Multiplication) {
+              firstFactor = firstFactor.childAtIndex(0);
+            }
+            if (firstFactor.type() == ExpressionNode::Type::Power) {
+              Expression exp = firstFactor.childAtIndex(1);
+              firstFactor = firstFactor.childAtIndex(0);
+              assert(exp.type() == ExpressionNode::Type::Rational && static_cast<Rational &>(exp).isInteger());
+              Integer expInt = static_cast<Rational &>(exp).signedIntegerNumerator();
+              if (expInt.isLowerThan(Integer(Integer::k_maxExtractableInteger))) {
+                exponent = expInt.extractedInt();
+              } else {
+                // The exponent is too large to be extracted, so do not try to use it.
+                exponent = 0;
+              }
+            }
+            assert(firstFactor.type() == ExpressionNode::Type::Unit);
+            // Choose its multiple and update value accordingly
+            if (exponent != 0) {
+              static_cast<Unit&>(firstFactor).chooseBestMultipleForValue(value, exponent, reductionContext);
+            }
           }
-        }
-        assert(firstFactor.type() == ExpressionNode::Type::Unit);
-        // Choose its multiple and update value accordingly
-        if (exponent != 0) {
-          static_cast<Unit&>(firstFactor).chooseBestMultipleForValue(value, exponent, reductionContext);
+          resultWithoutUnit = Float<double>::Builder(value);
         }
         // Build final Expression
-        result = Multiplication::Builder(Float<double>::Builder(value), units);
+        result = Multiplication::Builder(resultWithoutUnit, units);
         static_cast<Multiplication &>(result).mergeMultiplicationChildrenInPlace();
       }
     }
diff --git a/poincare/test/simplification.cpp b/poincare/test/simplification.cpp
index 89288f8f1..5c4c53fde 100644
--- a/poincare/test/simplification.cpp
+++ b/poincare/test/simplification.cpp
@@ -309,6 +309,16 @@ QUIZ_CASE(poincare_simplification_units) {
   assert_parsed_expression_simplify_to("_A^2×_s^4×_kg^(-1)×_m^(-3)", "_F×_m^\u0012-1\u0013"); // Vacuum magnetic permeability 𝝴0
   assert_parsed_expression_simplify_to("_kg×_s^(-3)×_K^(-4)", "_K^\u0012-4\u0013×_kg×_s^\u0012-3\u0013"); // Stefan–Boltzmann constant _W×_m^-2×_K^-4
 
+  /* Keep units for 0, infinity float results, Remove unit for undefined
+   * expression */
+  //assert_parsed_expression_simplify_to("0_s", "0_s");
+  assert_parsed_expression_simplify_to("inf×_s", "inf×_s");
+  //assert_parsed_expression_simplify_to("-inf×_s", "-inf×_s");
+  //assert_parsed_expression_simplify_to("2_s+3_s-5_s", "0_s");
+  assert_parsed_expression_simplify_to("normcdf(0,20,3)×_s", "0×_s");
+  //assert_parsed_expression_simplify_to("log(0)×_s", "-inf×_s");
+  assert_parsed_expression_simplify_to("log(undef)*_s", "undef");
+
   /* Units with invalid exponent */
   assert_parsed_expression_simplify_to("_s^(1/2)", "undef");