Answer: 5/66 (I'm so sorry if this is wrong)
Step-by-step explanation: First you divide 10 and 3 3/4. 10 ÷ 3 3/4 = 0.0757575757575.
To turn that back into to a fraction, let X equal the decimal number
Equation 1:
X = 0.0757575757575 (1)
With 12 digits in the repeating decimal group,
create a second equation by multiplying
both sides by 1012 = 1000000000000
Equation 2:
1000000000000X = 75757575757.5757575757575 (2)
Subtract equation (1) from equation (2)
1000000000000X = 75757575757.5757575757575...
X = 0.0757575757575...
999999999999X = 75757575757.5
We get
999999999999X = 75757575757.5
Solve for X
X = 75757575757.5/999999999999
Multiply to eliminate 1 decimal places.
Here you multiply top and bottom by 1 10's
= 101 = 10
75757575757.5/999999999999 × 10/10 = 757575757575/9999999999990
Find the Greatest Common Factor (GCF) of 757575757575 and 9999999999990, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 151515151515,
757575757575/9999999999990 ÷ 151515151515/151515151515 = 5/66
Therefore
X = 5/66
In conclusion,
0.0757575757575 = 5/66
