Convert the following repeating decimal to a fraction in simplest form.
.75
To convert a repeating decimal to a fraction, we need to first understand the process behind it. Let's consider the number .75.
In this case, we can see that the repeating decimal has two digits after the decimal point, namely 7 and 5. To convert this to a fraction, we can set up an equation where the repeating decimal is represented by variable x:
x = .75
To eliminate the repeating part, we can multiply both sides of the equation by 100, since there are two digits after the decimal point. This will shift the decimal point two places to the right, giving us:
100x = 75
Now, we can solve for x by dividing both sides of the equation by 100:
x = 75 / 100
Simplifying the fraction, we can divide the numerator and denominator by their greatest common divisor (which is 25 in this case):
x = (3 * 25) / (4 * 25)
This gives us:
x = 3 / 4
Therefore, the fraction equivalent of the repeating decimal .75 is 3/4.