How do you write 730.48101010 (10 is repeating) as a ratio of integers?

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Answer 1 · 2015-04-07T12:27:04

Let #x =730.48101010...# ------(1)

We multiply both sides of (1) with 100

#100x = 73048.101010...# ------(2)

We multiply both sides of (1) with 10000

#10000x = 7304810.101010...# ------(3)

We can subtract equation (2) from (3) to get rid of the decimal part

#10000x-100x = 7304810.101010... - 73048.101010...#

#9,900x = 7,231,762#

#x = 7231762/9900#

#730.4810101010... = 7231762/9900#
(Ratio of Integers/Rational Number)