How can you write 1.2244444444444444.... as a fraction?

1 Answer
Jun 28, 2015

Answer:

#1.2244444... = 1102/900 = 551/450#

Explanation:

If you see a single repeating digit, try multiplying by #9# first:

#1.2244444... * 9 = 11.02#

To make this into an integer just multiply by #100#

#11.02 * 100 = 1102#

So:

#1.2244444... * 900 = 1102#

Divide both sides by #900# to get:

#1.2244444... = 1102 / 900#

Actually both #1102# and #900# are even, so divide top and bottom by #2# to get:

#1.2244444... = 551 / 450#

Incidentally, I don't know if it's still popular, but there's a notation for repeating decimals, where you place a dot or dots above digits as follows:

#1.22dot(4)# to mean #1.2244444...#

Or if you have a repeating pattern of more than one digit, use a dot to mark each end of the repeating pattern, so:

#1/7 = 0.dot(1)4285dot(7)#

Perhaps you just did not know how to get Socratic to display this.