Convert 0.72¯¯¯¯¯ to a rational number in simplest form.

Answer 1

To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number, we can call it x. Then, we multiply x by a power of 10 to remove the repeating decimal. Let's multiply x by 100:

100x = 72.72¯¯¯¯¯

Next, we subtract x from 100x:

100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72

Dividing both sides of the equation by 99, we get:

x = 72/99

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:

x = (72/9) / (99/9)
x = 8/11

Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 8/11 in simplest form.

Answer 2

wait nvm i answered question before with 0.72¯¯¯¯¯, i shouldve wrote that instead.

Answer 3

No problem! To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can call it x. Then, we can multiply x by a power of 10 to eliminate the repeating decimal. Since there are two repeating digits, we'll multiply x by 100:

100x = 72.72¯¯¯¯¯

Next, we subtract x from 100x:

100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72

Now, divide both sides of the equation by 99:

x = 72/99

To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:

x = (72/9) / (99/9)
x = 8/11

Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 8/11 in simplest form.