diff --git a/Doc/library/decimal.rst b/Doc/library/decimal.rst
index e194649..7a64973 100644
--- a/Doc/library/decimal.rst
+++ b/Doc/library/decimal.rst
@@ -621,6 +621,13 @@
       Return :const:`True` if the argument is either positive or negative
       infinity and :const:`False` otherwise.
 
+   .. method:: is_integer()
+
+      Return :const:`True` if the argument is a finite integral value and
+      :const:`False` otherwise.
+
+      .. versionadded:: 3.10
+
    .. method:: is_nan()
 
       Return :const:`True` if the argument is a (quiet or signaling) NaN and
@@ -1215,6 +1222,13 @@
       Returns ``True`` if *x* is infinite; otherwise returns ``False``.
 
 
+   .. method:: is_integer(x)
+
+      Returns ``True`` if *x* is finite and integral; otherwise
+      returns ``False``.
+
+      .. versionadded:: 3.10
+
    .. method:: is_nan(x)
 
       Returns ``True`` if *x* is a qNaN or sNaN; otherwise returns ``False``.
diff --git a/Doc/library/numbers.rst b/Doc/library/numbers.rst
index 1b59495..5d49f5e 100644
--- a/Doc/library/numbers.rst
+++ b/Doc/library/numbers.rst
@@ -49,19 +49,30 @@
    numbers.
 
    In short, those are: a conversion to :class:`float`, :func:`math.trunc`,
-   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``,
-   ``%``, ``<``, ``<=``, ``>``, and ``>=``.
+   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`,
+   :func:`~Real.is_integer`, ``//``, ``%``, ``<``, ``<=``, ``>``, and ``>=``.
 
    Real also provides defaults for :func:`complex`, :attr:`~Complex.real`,
    :attr:`~Complex.imag`, and :meth:`~Complex.conjugate`.
 
+   .. method:: is_integer()
+
+      Returns :const:`True` if this number has a finite and integral value,
+      otherwise :const:`False`.  This is a default implementation which
+      relies on successful conversion to :class:`int`. It may be overridden
+      in subclasses (such as it is in :class:`float`) for better performance,
+      or to handle special values such as NaN which are not
+      convertible to :class:`int`.
+
+      .. versionadded:: 3.10
+
 
 .. class:: Rational
 
    Subtypes :class:`Real` and adds
    :attr:`~Rational.numerator` and :attr:`~Rational.denominator` properties, which
-   should be in lowest terms. With these, it provides a default for
-   :func:`float`.
+   should be in lowest terms. With these, it provides defaults for
+   :func:`float` and :func:`~Real.is_integer`.
 
    .. attribute:: numerator
 
@@ -75,9 +86,10 @@
 .. class:: Integral
 
    Subtypes :class:`Rational` and adds a conversion to :class:`int`.  Provides
-   defaults for :func:`float`, :attr:`~Rational.numerator`, and
-   :attr:`~Rational.denominator`.  Adds abstract methods for ``**`` and
-   bit-string operations: ``<<``, ``>>``, ``&``, ``^``, ``|``, ``~``.
+   defaults for :func:`float`, :attr:`~Rational.numerator`,
+   :attr:`~Rational.denominator`, and :func:`~Real.is_integer`.  Adds abstract
+   methods for ``**`` and bit-string operations: ``<<``, ``>>``, ``&``, ``^``,
+   ``|``, ``~``.
 
 
 Notes for type implementors
diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst
index 0ffe7b7..62f39da 100644
--- a/Doc/library/stdtypes.rst
+++ b/Doc/library/stdtypes.rst
@@ -310,6 +310,10 @@
 +---------------------+---------------------------------+---------+--------------------+
 | ``x ** y``          | *x* to the power *y*            | \(5)    |                    |
 +---------------------+---------------------------------+---------+--------------------+
+| ``x.is_integer()``  | ``True`` if *x* has a finite    |         | :func:`~numbers\   |
+|                     | and integral value, otherwise   |         | .Real.is_integer`  |
+|                     | ``False``.                      |         |                    |
++---------------------+---------------------------------+---------+--------------------+
 
 .. index::
    triple: operations on; numeric; types
@@ -583,16 +587,6 @@
    :exc:`OverflowError` on infinities and a :exc:`ValueError` on
    NaNs.
 
-.. method:: float.is_integer()
-
-   Return ``True`` if the float instance is finite with integral
-   value, and ``False`` otherwise::
-
-      >>> (-2.0).is_integer()
-      True
-      >>> (3.2).is_integer()
-      False
-
 Two methods support conversion to
 and from hexadecimal strings.  Since Python's floats are stored
 internally as binary numbers, converting a float to or from a
diff --git a/Lib/_pydecimal.py b/Lib/_pydecimal.py
index ab989e5..8c0ef57 100644
--- a/Lib/_pydecimal.py
+++ b/Lib/_pydecimal.py
@@ -3164,6 +3164,12 @@
         """Return True if self is a zero; otherwise return False."""
         return not self._is_special and self._int == '0'
 
+    def is_integer(self):
+        """Return True is self is finite and integral; otherwise False."""
+        if self._is_special:
+            return False
+        return self.to_integral_value(rounding=ROUND_FLOOR) == self
+
     def _ln_exp_bound(self):
         """Compute a lower bound for the adjusted exponent of self.ln().
         In other words, compute r such that self.ln() >= 10**r.  Assumes
@@ -4659,6 +4665,25 @@
         a = _convert_other(a, raiseit=True)
         return a.is_zero()
 
+    def is_integer(self, a):
+        """Return True if the operand is integral; otherwise return False.
+
+        >>> ExtendedContext.is_integer(Decimal('0'))
+        True
+        >>> ExtendedContext.is_integer(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_integer(Decimal('-0E+2'))
+        True
+        >>> ExtendedContext.is_integer(Decimal('-0.5'))
+        False
+        >>> ExtendedContext.is_integer(Decimal('NaN'))
+        False
+        >>> ExtendedContext.is_integer(10)
+        True
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.is_integer()
+
     def ln(self, a):
         """Returns the natural (base e) logarithm of the operand.
 
diff --git a/Lib/numbers.py b/Lib/numbers.py
index ed815ef..0634f62 100644
--- a/Lib/numbers.py
+++ b/Lib/numbers.py
@@ -148,7 +148,7 @@
     """To Complex, Real adds the operations that work on real numbers.
 
     In short, those are: a conversion to float, trunc(), divmod,
-    %, <, <=, >, and >=.
+    is_integer, %, <, <=, >, and >=.
 
     Real also provides defaults for the derived operations.
     """
@@ -242,6 +242,17 @@
         """self <= other"""
         raise NotImplementedError
 
+    def is_integer(self):
+        """Return True if the Real is integral; otherwise return False.
+
+        This default implementation can be overridden in subclasses
+        for performance reasons or to deal with values such as NaN,
+        which would otherwise cause an exception to be raised.
+        """
+        # Although __int__ is not defined at this level, the int
+        # constructor falls back to __trunc__, which we do have.
+        return self == int(self)
+
     # Concrete implementations of Complex abstract methods.
     def __complex__(self):
         """complex(self) == complex(float(self), 0)"""
@@ -290,6 +301,10 @@
         """
         return self.numerator / self.denominator
 
+    def is_integer(self):
+        """Return True if the Rational is integral; otherwise return False."""
+        return self.denominator == 1
+
 
 class Integral(Rational):
     """Integral adds a conversion to int and the bit-string operations."""
@@ -386,4 +401,8 @@
         """Integers have a denominator of 1."""
         return 1
 
+    def is_integer(self):
+        """Return True; all Integrals represent an integral value."""
+        return True
+
 Integral.register(int)
diff --git a/Lib/test/decimaltestdata/extra.decTest b/Lib/test/decimaltestdata/extra.decTest
index b630d8e..2f0719e 100644
--- a/Lib/test/decimaltestdata/extra.decTest
+++ b/Lib/test/decimaltestdata/extra.decTest
@@ -2346,6 +2346,24 @@
 bool2097 iszero -sNaN -> 0
 bool2098 iszero sNaN123 -> 0
 bool2099 iszero -sNaN123 -> 0
+bool2100 is_integer -1.0 -> 1
+bool2101 is_integer 0.0 -> 1
+bool2102 is_integer 1.0 -> 1
+bool2103 is_integer 42 -> 1
+bool2104 is_integer 1e2 -> 1
+bool2105 is_integer 1.5 -> 0
+bool2106 is_integer 1e-2 -> 0
+bool2107 is_integer NaN -> 0
+bool2109 is_integer -NaN -> 0
+bool2110 is_integer NaN123 -> 0
+bool2111 is_integer -NaN123 -> 0
+bool2112 is_integer sNaN -> 0
+bool2113 is_integer -sNaN -> 0
+bool2114 is_integer sNaN123 -> 0
+bool2115 is_integer -sNaN123 -> 0
+bool2116 is_integer Infinity -> 0
+bool2117 is_integer -Infinity -> 0
+
 
 ------------------------------------------------------------------------
 -- The following tests (pwmx0 through pwmx440) are for the            --
diff --git a/Lib/test/test_bool.py b/Lib/test/test_bool.py
index 7b3a385..bc201e1 100644
--- a/Lib/test/test_bool.py
+++ b/Lib/test/test_bool.py
@@ -354,6 +354,11 @@
         self.assertIs(type(False.real), int)
         self.assertIs(type(False.imag), int)
 
+    def test_always_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into bool
+        self.assertTrue(all(b.is_integer() for b in (False, True)))
+
+
 def test_main():
     support.run_unittest(BoolTest)
 
diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py
index dbd58e8..efb41fd 100644
--- a/Lib/test/test_decimal.py
+++ b/Lib/test/test_decimal.py
@@ -276,6 +276,7 @@
                                  'is_snan',
                                  'is_subnormal',
                                  'is_zero',
+                                 'is_integer',
                                  'same_quantum')
 
     def read_unlimited(self, v, context):
@@ -2726,6 +2727,7 @@
             self.assertRaises(TypeError, D(1).is_snan, context=xc)
             self.assertRaises(TypeError, D(1).is_signed, context=xc)
             self.assertRaises(TypeError, D(1).is_zero, context=xc)
+            self.assertRaises(TypeError, D(1).is_integer, context=xc)
 
             self.assertFalse(D("0.01").is_normal(context=xc))
             self.assertTrue(D("0.01").is_subnormal(context=xc))
@@ -3197,6 +3199,15 @@
         self.assertEqual(c.is_zero(10), d)
         self.assertRaises(TypeError, c.is_zero, '10')
 
+    def test_is_integer(self):
+        Decimal = self.decimal.Decimal
+        Context = self.decimal.Context
+
+        c = Context()
+        b = c.is_integer(Decimal(10))
+        self.assertEqual(c.is_integer(10), b)
+        self.assertRaises(TypeError, c.is_integer, '10')
+
     def test_ln(self):
         Decimal = self.decimal.Decimal
         Context = self.decimal.Context
@@ -4360,6 +4371,19 @@
             self.assertTrue(Decimal("-1").is_signed())
             self.assertTrue(Decimal("0").is_zero())
             self.assertTrue(Decimal("0").is_zero())
+            self.assertTrue(Decimal("-1").is_integer())
+            self.assertTrue(Decimal("0").is_integer())
+            self.assertTrue(Decimal("1").is_integer())
+            self.assertTrue(Decimal("42").is_integer())
+            self.assertTrue(Decimal("1e2").is_integer())
+            self.assertFalse(Decimal("1.5").is_integer())
+            self.assertFalse(Decimal("1e-2").is_integer())
+            self.assertFalse(Decimal("NaN").is_integer())
+            self.assertFalse(Decimal("-NaN").is_integer())
+            self.assertFalse(Decimal("sNaN").is_integer())
+            self.assertFalse(Decimal("-sNaN").is_integer())
+            self.assertFalse(Decimal("Inf").is_integer())
+            self.assertFalse(Decimal("-Inf").is_integer())
 
         # Copy
         with localcontext() as c:
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 0845f79..811b58f 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -724,6 +724,17 @@
         self.assertEqual(type(f.numerator), myint)
         self.assertEqual(type(f.denominator), myint)
 
+    def test_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into Fraction
+        self.assertTrue(F(-1, 1).is_integer())
+        self.assertTrue(F(0, 1).is_integer())
+        self.assertTrue(F(1, 1).is_integer())
+        self.assertTrue(F(42, 1).is_integer())
+        self.assertTrue(F(2, 2).is_integer())
+        self.assertTrue(F(8, 4).is_integer())
+        self.assertFalse(F(1, 2).is_integer())
+        self.assertFalse(F(1, 3).is_integer())
+        self.assertFalse(F(2, 3).is_integer())
 
 if __name__ == '__main__':
     unittest.main()
diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index c97842b..669826c 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -1381,6 +1381,10 @@
             self.assertEqual(type(numerator), int)
             self.assertEqual(type(denominator), int)
 
+    def test_int_always_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into int
+        self.assertTrue(all(x.is_integer() for x in (-1, 0, 1, 42)))
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Lib/test/test_numeric_tower.py b/Lib/test/test_numeric_tower.py
index c54dedb..4e46aac 100644
--- a/Lib/test/test_numeric_tower.py
+++ b/Lib/test/test_numeric_tower.py
@@ -6,6 +6,7 @@
 import sys
 import operator
 
+from numbers import Real, Rational, Integral
 from decimal import Decimal as D
 from fractions import Fraction as F
 
@@ -198,5 +199,35 @@
                 self.assertRaises(TypeError, op, v, z)
 
 
+class IsIntegerTest(unittest.TestCase):
+
+    def test_real_is_integer(self):
+        self.assertTrue(Real.is_integer(-1.0))
+        self.assertTrue(Real.is_integer(0.0))
+        self.assertTrue(Real.is_integer(1.0))
+        self.assertTrue(Real.is_integer(42.0))
+
+        self.assertFalse(Real.is_integer(-0.5))
+        self.assertFalse(Real.is_integer(4.2))
+
+    def test_rational_is_integer(self):
+        self.assertTrue(Rational.is_integer(F(-1, 1)))
+        self.assertTrue(Rational.is_integer(F(0, 1)))
+        self.assertTrue(Rational.is_integer(F(1, 1)))
+        self.assertTrue(Rational.is_integer(F(42, 1)))
+        self.assertTrue(Rational.is_integer(F(2, 2)))
+        self.assertTrue(Rational.is_integer(F(8, 4)))
+
+        self.assertFalse(Rational.is_integer(F(1, 2)))
+        self.assertFalse(Rational.is_integer(F(1, 3)))
+        self.assertFalse(Rational.is_integer(F(2, 3)))
+
+    def test_integral_is_integer(self):
+        self.assertTrue(Integral.is_integer(-1))
+        self.assertTrue(Integral.is_integer(0))
+        self.assertTrue(Integral.is_integer(1))
+        self.assertTrue(Integral.is_integer(1729))
+
+
 if __name__ == '__main__':
     unittest.main()
diff --git a/Misc/ACKS b/Misc/ACKS
index 85001da..9be0e77 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -1611,6 +1611,7 @@
 Ville Skyttä
 Michael Sloan
 Nick Sloan
+Robert Smallshire
 Václav Šmilauer
 Allen W. Smith
 Christopher Smith
diff --git a/Misc/NEWS.d/next/Core and Builtins/2018-03-15-11-51-36.bpo-26680.wOWYps.rst b/Misc/NEWS.d/next/Core and Builtins/2018-03-15-11-51-36.bpo-26680.wOWYps.rst
new file mode 100644
index 0000000..93325ff
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2018-03-15-11-51-36.bpo-26680.wOWYps.rst
@@ -0,0 +1,2 @@
+The int type now supports the x.is_integer() method for compatibility with
+float.
diff --git a/Misc/NEWS.d/next/Library/2018-03-15-11-55-04.bpo-26680.eKAi85.rst b/Misc/NEWS.d/next/Library/2018-03-15-11-55-04.bpo-26680.eKAi85.rst
new file mode 100644
index 0000000..8b2e818
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-03-15-11-55-04.bpo-26680.eKAi85.rst
@@ -0,0 +1,3 @@
+The x.is_integer() method is incorporated into the abstract types of the
+numeric tower, Real, Rational and Integral, with appropriate default
+implementations.
diff --git a/Misc/NEWS.d/next/Library/2018-03-15-11-56-48.bpo-26680.Udkhn4.rst b/Misc/NEWS.d/next/Library/2018-03-15-11-56-48.bpo-26680.Udkhn4.rst
new file mode 100644
index 0000000..df75e08
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-03-15-11-56-48.bpo-26680.Udkhn4.rst
@@ -0,0 +1,2 @@
+The d.is_integer() method is added to the Decimal type, for compatibility
+with other number types.
diff --git a/Modules/_decimal/_decimal.c b/Modules/_decimal/_decimal.c
index e7c44ac..5200b1a 100644
--- a/Modules/_decimal/_decimal.c
+++ b/Modules/_decimal/_decimal.c
@@ -4138,6 +4138,7 @@
 Dec_BoolFunc(mpd_issnan)
 Dec_BoolFunc(mpd_issigned)
 Dec_BoolFunc(mpd_iszero)
+Dec_BoolFunc(mpd_isinteger)
 
 /* Boolean functions, optional context arg */
 Dec_BoolFuncVA(mpd_isnormal)
@@ -4772,6 +4773,7 @@
   { "is_snan", dec_mpd_issnan, METH_NOARGS, doc_is_snan },
   { "is_signed", dec_mpd_issigned, METH_NOARGS, doc_is_signed },
   { "is_zero", dec_mpd_iszero, METH_NOARGS, doc_is_zero },
+  { "is_integer", dec_mpd_isinteger, METH_NOARGS, doc_is_integer},
 
   /* Boolean functions, optional context arg */
   { "is_normal", (PyCFunction)(void(*)(void))dec_mpd_isnormal, METH_VARARGS|METH_KEYWORDS, doc_is_normal },
@@ -5183,6 +5185,7 @@
 DecCtx_BoolFunc_NO_CTX(mpd_issigned)
 DecCtx_BoolFunc_NO_CTX(mpd_issnan)
 DecCtx_BoolFunc_NO_CTX(mpd_iszero)
+DecCtx_BoolFunc_NO_CTX(mpd_isinteger)
 
 static PyObject *
 ctx_iscanonical(PyObject *context UNUSED, PyObject *v)
@@ -5464,6 +5467,7 @@
   { "is_snan", ctx_mpd_issnan, METH_O, doc_ctx_is_snan },
   { "is_subnormal", ctx_mpd_issubnormal, METH_O, doc_ctx_is_subnormal },
   { "is_zero", ctx_mpd_iszero, METH_O, doc_ctx_is_zero },
+  { "is_integer", ctx_mpd_isinteger, METH_O, doc_ctx_is_integer },
 
   /* Functions with a single decimal argument */
   { "_apply", PyDecContext_Apply, METH_O, NULL }, /* alias for apply */
@@ -6097,5 +6101,3 @@
 
     return NULL; /* GCOV_NOT_REACHED */
 }
-
-
diff --git a/Modules/_decimal/docstrings.h b/Modules/_decimal/docstrings.h
index f7fd6e7..bd602ab 100644
--- a/Modules/_decimal/docstrings.h
+++ b/Modules/_decimal/docstrings.h
@@ -260,6 +260,11 @@
 otherwise.\n\
 \n");
 
+PyDoc_STRVAR(doc_is_integer,
+"is_integer($self, /)\n--\n\n\
+Return True if the argument is finite and integral, otherwise False.\n\
+\n");
+
 PyDoc_STRVAR(doc_ln,
 "ln($self, /, context=None)\n--\n\n\
 Return the natural (base e) logarithm of the operand. The function always\n\
@@ -685,6 +690,11 @@
 Return True if x is a zero, False otherwise.\n\
 \n");
 
+PyDoc_STRVAR(doc_ctx_is_integer,
+"is_integer($self, x, /)\n--\n\n\
++Return True if x is finite and integral, False otherwise.\n\
++\n");
+
 PyDoc_STRVAR(doc_ctx_ln,
 "ln($self, x, /)\n--\n\n\
 Return the natural (base e) logarithm of x.\n\
@@ -879,6 +889,3 @@
 
 
 #endif /* DOCSTRINGS_H */
-
-
-
diff --git a/Objects/clinic/longobject.c.h b/Objects/clinic/longobject.c.h
index 4bd47b1..16e6f7e 100644
--- a/Objects/clinic/longobject.c.h
+++ b/Objects/clinic/longobject.c.h
@@ -121,6 +121,24 @@
     return return_value;
 }
 
+PyDoc_STRVAR(int_is_integer__doc__,
+"is_integer($self, /)\n"
+"--\n"
+"\n"
+"Returns True for all integers.");
+
+#define INT_IS_INTEGER_METHODDEF    \
+    {"is_integer", (PyCFunction)int_is_integer, METH_NOARGS, int_is_integer__doc__},
+
+static PyObject *
+int_is_integer_impl(PyObject *self);
+
+static PyObject *
+int_is_integer(PyObject *self, PyObject *Py_UNUSED(ignored))
+{
+    return int_is_integer_impl(self);
+}
+
 PyDoc_STRVAR(int___sizeof____doc__,
 "__sizeof__($self, /)\n"
 "--\n"
@@ -367,4 +385,4 @@
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=ea18e51af5b53591 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=022614978e2fcdf3 input=a9049054013a1b77]*/
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 92514d4..bc5b49d 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -5234,6 +5234,19 @@
 }
 
 /*[clinic input]
+int.is_integer
+
+Returns True for all integers.
+[clinic start generated code]*/
+
+static PyObject *
+int_is_integer_impl(PyObject *self)
+/*[clinic end generated code: output=90f8e794ce5430ef input=1c1a86957301d26d]*/
+{
+    Py_RETURN_TRUE;
+}
+
+/*[clinic input]
 int.__sizeof__ -> Py_ssize_t
 
 Returns size in memory, in bytes.
@@ -5547,6 +5560,7 @@
     {"__ceil__",        long_long_meth, METH_NOARGS,
      "Ceiling of an Integral returns itself."},
     INT___ROUND___METHODDEF
+    INT_IS_INTEGER_METHODDEF
     INT___GETNEWARGS___METHODDEF
     INT___FORMAT___METHODDEF
     INT___SIZEOF___METHODDEF