Question
What is 0.72 repeated two a rational number in simple
Answers
GPT 3.5
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not equal to zero.
To express 0.72 repeated as a rational number, we need to convert it into a fraction. Let's call the number x:
x = 0.727272...
To remove the repeating decimals, we can subtract x from 100x:
100x = 72.727272...
- x = 0.727272...
Next, we subtract the two equations to eliminate the repeating portion:
99x = 72
x = 72/99
We can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor (GCD):
The GCD of 72 and 99 is 9.
72 ÷ 9 = 8
99 ÷ 9 = 11
So, the rational number representation of 0.72 repeated is 8/11.
To express 0.72 repeated as a rational number, we need to convert it into a fraction. Let's call the number x:
x = 0.727272...
To remove the repeating decimals, we can subtract x from 100x:
100x = 72.727272...
- x = 0.727272...
Next, we subtract the two equations to eliminate the repeating portion:
99x = 72
x = 72/99
We can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor (GCD):
The GCD of 72 and 99 is 9.
72 ÷ 9 = 8
99 ÷ 9 = 11
So, the rational number representation of 0.72 repeated is 8/11.