Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(
0.72¯¯¯¯¯ can be represented as the decimal 0.727272..., where the repeating decimal pattern is 72. To convert this to a rational number in simplest form, we can let x = 0.727272...
Then, 100x = 72.727272..., which can be written as:
100x = 72 + 0.727272...
100x = 72 + x
99x = 72
x = 72/99
Therefore, 0.727272... as a rational number in simplest form is 72/99.
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the concept of repeating decimals.
Let's represent 0.72¯¯¯¯¯ as x.
To remove the repeating part, we can multiply both sides of the equation by a power of 10 equal to the number of repeating digits.
In this case, we have 2 repeating digits (72), so we will multiply by 100:
100x = 72.¯¯¯¯¯
Now, we can subtract the original equation from the new equation:
100x - x = 72.¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Finally, we can simplify the rational number by dividing both numerator and denominator by the greatest common divisor (GCD):
GCD(72, 99) = 9
Dividing both numerator and denominator by 9, we get:
72 ÷ 9 / 99 ÷ 9
8 / 11
Therefore, 0.72¯¯¯¯¯ can be simplified to the rational number 8/11 in simplest form.