Finite decimal values can be converted to fractions much more easily than repeating decimals. To calculate the value of a repeating decimal we need to setup equivalent algebraic equations where our variable represents the value of the fraction, subtract the equations from each other to eliminate the repeating decimal value, and then solve for x.
Answer and Explanation:
As a fraction 0.8 (8 repeating) is
8
9
.
To calculate the fraction value of 0.8 repeating we multiply it by 10 to get an 8 to the left of the decimal. This gives us:
x = 0.8888... and
10x = 8.888...
We can now subtract these equations to solve for the value of x in our equations:
10
x
=
8.888...
−
x
=
0.8888...
−
−
−
−
−
−
−
−
−
9
x
=
8
We can now divide both sides by 9 to find hte value of x:
9
x
=
8
9
x
9
=
8
9
x
=
8
9