Convert the following repeating decimal to a fraction in simplest form.
point, 9, start overline, 5, end overline
.9
5
To convert the repeating decimal .95 to a fraction, we can use the concept of geometric series.
Let x = .95
Then, 100x = 95.5555...
By subtracting the two equations, we get:
100x - x = 95.5555... - .95
99x = 95.6055
Dividing both sides by 99, we find:
x = 95.6055 / 99
Now we can express this decimal as a fraction:
x = 956055 / 990000
However, we still need to simplify this fraction. To do so, we can divide both numerator and denominator by their greatest common divisor.
The greatest common divisor of 956055 and 990000 is 45, so by dividing both terms by 45, we get:
x = 21223 / 22000
Therefore, the repeating decimal .959595... can be expressed as the fraction 21223/22000 in simplest form.