Write the recurring decimal 0.473737373... as a fraction.

Step-by-step explanation:

We require 2 equations with the repeating digits after the decimal point.

By subtracting the 2 equations eliminates the repeating digits.

let x = 0.47373737.....

Multiply both sides by 100 and 10000, that is

100x = 47.3737... → (1)

10000x = 4737.3737.... → (2)

Subtract (1) from (2)

9900x = 4690 ( divide both sides by 9900 )

x = = ← in simplest form

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3