4,720,000,000,000,000,000,000 in words is "four sextillion seven hundred twenty quintillion".
Here is a quick list of numbers and how many 0s they have:
Ten: 10 (1 zero)
Hundred: 100 (2 zeros)
Thousand: 1000 (3 zeros)
Ten thousand 10,000 (4 zeros)
Hundred thousand 100,000 (5 zeros)
Million 1,000,000 (6 zeros)
Billion 1,000,000,000 (9 zeros)
Trillion 1,000,000,000,000 (12 zeros)
Quadrillion 1,000,000,000,000,000 (15 zeros)
Quintillion 1,000,000,000,000,000,000 (18 zeros)
Sextillion 1,000,000,000,000,000,000,000 (21 zeros)
Septillion 1,000,000,000,000,000,000,000,000 (24 zeros)
Octillion 1,000,000,000,000,000,000,000,000,000 (27 zeros)
Nonillion 1,000,000,000,000,000,000,000,000,000,000 (30 zeros)
Decillion 1,000,000,000,000,000,000,000,000,000,000,000 (33 zeros)
This process can be continued indefinitely, but one has to stop somewhere. The name centillion (n = 100) has appeared in many dictionaries. A centillion is 10303 (1 followed by 303 zeroes) in the American system and a whopping 10600 (1 followed by 600 zeroes) in the European system.
Finally, there is the googol, the number 10100 (1 followed by 100 zeroes). Invented more for fun than for use, the googol lies outside the regular naming systems. The googol equals 10 duotrigintillion in the American system, 10 sexdecilliard in the European system, and 10 triacontatrillion in the proposed Greek-based system.
The googolplex (1 followed by a googol of zeroes) is far larger than any of the numbers discussed here. Read more at UNC.edu.