Answer:
5/18
Explaination:
Let X equal the decimal number
Equation 1:
X=0.2777¯¯¯¯¯¯¯¯(1)
With 3 digits in the repeating decimal group,
create a second equation by multiplying
both sides by 103 = 1000
Equation 2:
1000X=277.7777¯¯¯¯¯¯¯¯(2)
Subtract equation (1) from equation (2)
1000XX999X===277.7777...0.2777...277.5
We get
999X=277.5
Solve for X
X=277.5999
Multiply to eliminate 1 decimal places.
Here you multiply top and bottom by 1 10's
= 101 = 10
277.5999×1010=27759990
Find the Greatest Common Factor (GCF) of 2775 and 9990, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 555,
2775÷5559990÷555=518
Therefore
X=518
In conclusion,
0.2777¯¯¯¯¯¯¯¯=518