diff --git a/poincare/src/power.cpp b/poincare/src/power.cpp
index d66ab2273..f5a04957c 100644
--- a/poincare/src/power.cpp
+++ b/poincare/src/power.cpp
@@ -5,7 +5,6 @@
 #include <poincare/constant.h>
 #include <poincare/cosine.h>
 #include <poincare/division.h>
-#include <poincare/float.h>
 #include <poincare/horizontal_layout.h>
 #include <poincare/infinity.h>
 #include <poincare/matrix.h>
@@ -398,6 +397,10 @@ Expression Power::shallowReduce(ExpressionNode::ReductionContext reductionContex
         // The exponent must be an Integer
         return replaceWithUndefinedInPlace();
       }
+      if (parent().isUninitialized() && base.type() == ExpressionNode::Type::Unit) {
+        // A Power of Unit must not be orphan
+        return Multiplication::Builder(Rational::Builder(1), *this);
+      }
     }
   }
 
@@ -979,15 +982,6 @@ Expression Power::shallowBeautify(ExpressionNode::ReductionContext reductionCont
     replaceWithInPlace(result);
     return result;
   }
-
-  // Step 4: Force Float(1) in front of an orphan Power of Unit
-  if (parent().isUninitialized() && childAtIndex(0).type() == ExpressionNode::Type::Unit) {
-    Multiplication m = Multiplication::Builder(Float<double>::Builder(1.0));
-    replaceWithInPlace(m);
-    m.addChildAtIndexInPlace(*this, 1, 1);
-    return std::move(m);
-  }
-
   return *this;
 }
 
diff --git a/poincare/src/unit.cpp b/poincare/src/unit.cpp
index d461ccb17..344654270 100644
--- a/poincare/src/unit.cpp
+++ b/poincare/src/unit.cpp
@@ -1,6 +1,5 @@
 #include <poincare/unit.h>
 #include <poincare/division.h>
-#include <poincare/float.h>
 #include <poincare/ieee754.h>
 #include <poincare/multiplication.h>
 #include <poincare/power.h>
@@ -310,19 +309,16 @@ Expression Unit::shallowReduce(ExpressionNode::ReductionContext reductionContext
     Expression multiplier = Power::Builder(Rational::Builder(10), Rational::Builder(prefixMultiplier)).shallowReduce(reductionContext);
     result = Multiplication::Builder(multiplier, result).shallowReduce(reductionContext);
   }
+  if (parent().isUninitialized() && result.type() == ExpressionNode::Type::Unit) {
+    // A Unit must not be orphan
+    result = Multiplication::Builder(Rational::Builder(1), result);
+  }
   replaceWithInPlace(result);
   return result;
 }
 
 Expression Unit::shallowBeautify(ExpressionNode::ReductionContext reductionContext) {
   Expression ancestor = parent();
-  // Force Float(1) in front of an orphan Unit
-  if (ancestor.isUninitialized()) {
-    Multiplication m = Multiplication::Builder(Float<double>::Builder(1.0));
-    replaceWithInPlace(m);
-    m.addChildAtIndexInPlace(*this, 1, 1);
-    return std::move(m);
-  }
   if (!ancestor.isUninitialized() && ancestor.type() == ExpressionNode::Type::Power) {
     ancestor = ancestor.parent();
   }