diff --git a/Lib/decimal.py b/Lib/decimal.py
index 4797a7d..e5329dd 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -1048,12 +1048,11 @@
         return sign + intpart + fracpart + exp
 
     def to_eng_string(self, context=None):
-        """Convert to engineering-type string.
+        """Convert to a string, using engineering notation if an exponent is needed.
 
-        Engineering notation has an exponent which is a multiple of 3, so there
-        are up to 3 digits left of the decimal place.
-
-        Same rules for when in exponential and when as a value as in __str__.
+        Engineering notation has an exponent which is a multiple of 3.  This
+        can leave up to 3 digits to the left of the decimal place and may
+        require the addition of either one or two trailing zeros.
         """
         return self.__str__(eng=True, context=context)
 
@@ -5339,9 +5338,29 @@
             return r
 
     def to_eng_string(self, a):
-        """Converts a number to a string, using scientific notation.
+        """Convert to a string, using engineering notation if an exponent is needed.
+
+        Engineering notation has an exponent which is a multiple of 3.  This
+        can leave up to 3 digits to the left of the decimal place and may
+        require the addition of either one or two trailing zeros.
 
         The operation is not affected by the context.
+
+        >>> ExtendedContext.to_eng_string(Decimal('123E+1'))
+        '1.23E+3'
+        >>> ExtendedContext.to_eng_string(Decimal('123E+3'))
+        '123E+3'
+        >>> ExtendedContext.to_eng_string(Decimal('123E-10'))
+        '12.3E-9'
+        >>> ExtendedContext.to_eng_string(Decimal('-123E-12'))
+        '-123E-12'
+        >>> ExtendedContext.to_eng_string(Decimal('7E-7'))
+        '700E-9'
+        >>> ExtendedContext.to_eng_string(Decimal('7E+1'))
+        '70'
+        >>> ExtendedContext.to_eng_string(Decimal('0E+1'))
+        '0.00E+3'
+
         """
         a = _convert_other(a, raiseit=True)
         return a.to_eng_string(context=self)