Convert the following repeating decimal to a fraction in simplest form.

Question

point, 7, start overline, 5, end overline
.7
5

Answer 1

To convert the decimal .75 to a fraction, we can use the formula for converting a decimal to a fraction. Let x represent the decimal:

x = .75

To remove the decimal, we can multiply both sides of the equation by 100 (since there are two decimal places):

100x = 75

Now we can convert the equation to a fraction:

100x/100 = 75/100

Simplifying the fraction:

x = 75/100

We can further simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 25:

x = (75/25)/(100/25)
x = 3/4

Therefore, the fraction equivalent of the repeating decimal .75 is 3/4.

Answer 2

Convert the following repeating decimal to a fraction in simplest form.
point, 7, start overline, 5, end overline

Answer 3

To convert the decimal .775 to a fraction, we can use the formula for converting a repeating decimal to a fraction. Let n represent the repeating part of the decimal, which in this case is 75:

x = .775

To remove the repeating part, we can multiply x by a power of 10 that has the same number of digits as the repeating part:

1000x = 775.775

Next, we subtract the original equation from this new equation:

1000x - x = 775.775 - .775

Simplifying:

999x = 775

Now we can convert the equation to a fraction:

999x/999 = 775/999

Simplifying the fraction:

x = 775/999

We can further simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 25:

x = (775/25)/(999/25)
x = 31/40

Therefore, the fraction equivalent of the repeating decimal .775 is 31/40.