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