Convert the following repeating decimal to a fraction in simplest form.
point, 5, start overline, 1, end overline.
To convert the repeating decimal "0.5̅1̅" to a fraction, let's denote it as x:
x = 0.51̅
First, we can multiply both sides of the equation by 1000 (since there are 3 digits recurring):
1000x = 515.151̅
Now, we subtract the original equation from the above equation to eliminate the recurring decimal:
1000x - x = 515.151̅ - 0.51̅
999x = 514.64
Next, we simplify the equation by dividing both sides by 999:
x = 514.64 / 999
To further simplify our fraction, we look for the greatest common divisor (GCD) between the numerator and denominator. In this case, they do not share any common factors other than 1:
GCD(514.64 , 999) = 1
Therefore, we cannot reduce the fraction any further.
Hence, the fraction equivalent to the repeating decimal 0.5̅1̅ is 514.64/999.
Convert the following repeating decimal to a fraction in simplest form.
point, 2, start overline, 1, end overline
.2
1
To convert the repeating decimal "0.2̅1̅" to a fraction, let's denote it as x:
x = 0.2̅1̅
First, we can multiply both sides of the equation by 100 (since there are 2 digits recurring):
100x = 21.1̅
Now, we subtract the original equation from the above equation to eliminate the recurring decimal:
100x - x = 21.1̅ - 0.2̅
99x = 21
Next, we simplify the equation by dividing both sides by 99:
x = 21 / 99 = 7 / 33
To further simplify our fraction, we look for the greatest common divisor (GCD) between the numerator and denominator. In this case, 7 is a prime number and does not have any common factors with 33:
GCD(7, 33) = 1
Therefore, we cannot reduce the fraction any further.
Hence, the fraction equivalent to the repeating decimal 0.2̅1̅ is 7/33.