Adding computer (python) language seemed to slow down my thinking, but actually helped me with organizing each step in order.

I kept getting 'fail' message, and fixed minor errors multiple times. For example, adding blank space between two words can be done by using + " " was forgotten a few times.

numberwords.py

@@ -15,19 +15,42 @@ TENS_NAMES = [
 ]
 
 def int_under_1000000_to_str(number):
-    return "umm..."
+    if number<1000:
+        return int_under_1000_to_str(number)
+    quotient,remainder=divide_with_remainder(number,1000)
+    Q1=int_under_1000_to_str(quotient) + " " + "thousand"
+    if remainder>0:
+        R1=int_under_1000_to_str(remainder)
+        return Q1 + " " + R1
+    return Q1
         
 def int_under_1000_to_str(number):
-    return "umm..."
+    if number<100:
+        return int_under_100_to_str(number)
+    quotient,remainder=divide_with_remainder(number,100)
+    Q1=int_under_10_to_str(quotient) + " " + "hundred"
+    if remainder>0:
+        R1=int_under_100_to_str(remainder)
+        return Q1 + " and " + R1
+    return Q1
 
 def int_under_100_to_str(number):
-    return "umm..."
+    if number<20:
+        return int_under_20_to_str(number)
+    quotient,remainder=divide_with_remainder(number,10)
+    tensname=TENS_NAMES[quotient]
+    if remainder>0:
+        onesname=int_under_10_to_str(remainder)
+        return tensname + "-" + onesname
+    return tensname
 
 def int_under_20_to_str(number):
-    return "umm..."
+    if number<10:
+        return int_under_10_to_str(number)
+    return TWEEN_AND_TEEN_NAMES[number-10]
 
 def int_under_10_to_str(number):
-    return "umm..."
+    return DIGIT_NAMES[number]
 
 def divide_with_remainder(dividend, divisor):
     """Divides one number by another, using whole-number division. 

test_numberwords.py

@@ -33,7 +33,7 @@ class TestIntToStr(unittest.TestCase):
         [int_under_1000000_to_str, 1001, 'one thousand one'], 
         [int_under_1000000_to_str, 1672, 'one thousand six hundred and seventy-two'], 
         [int_under_1000000_to_str, 10000, 'ten thousand'], 
-        [int_under_1000000_to_str, 588567, 'five hundred and ninety-eight thousand five hundred and sixty-seven'],
+        [int_under_1000000_to_str, 598567, 'five hundred and ninety-eight thousand five hundred and sixty-seven'],
     ]
 
     def test_converts_integer_to_string(self):