Question
What is 0.8 as a rational number
Answers
GPT 3.5
0.8 as a rational number is 8/10 or simplified further as 4/5.
What is 0.8 repeated 8 as a rational number
GPT 3.5
0.8 repeated 8, denoted as 0.88888888, can be represented as a rational number by setting it equal to the fraction x.
To convert the repeating decimal to a fraction, we will multiply both sides of the equation by 10^8 (a 1 followed by 8 zeros) to eliminate the repeating part:
10^8 * x = 8.88888888...
Next, we subtract the original equation from the equation multiplied by 10^8:
(10^8 * x) - x = 8.88888888 - 0.88888888
10^8 * x - x = 8
Simplifying the equation:
(10^8 - 1) * x = 8
To isolate x, we divide both sides of the equation by (10^8 - 1):
x = 8 / (10^8 - 1)
Thus, 0.8 repeated 8 can be represented as the fraction 8 / (10^8 - 1) in rational form.
To convert the repeating decimal to a fraction, we will multiply both sides of the equation by 10^8 (a 1 followed by 8 zeros) to eliminate the repeating part:
10^8 * x = 8.88888888...
Next, we subtract the original equation from the equation multiplied by 10^8:
(10^8 * x) - x = 8.88888888 - 0.88888888
10^8 * x - x = 8
Simplifying the equation:
(10^8 - 1) * x = 8
To isolate x, we divide both sides of the equation by (10^8 - 1):
x = 8 / (10^8 - 1)
Thus, 0.8 repeated 8 can be represented as the fraction 8 / (10^8 - 1) in rational form.