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

Answer 1

To convert 0.72¯¯¯¯¯ to a rational number in simplest form, let's call it x.

To convert the repeating decimal to a fraction, we can use the method of algebraic manipulation.
Let's multiply both sides of the equation x = 0.72¯¯¯¯¯ by 100, which moves the decimal point two places to the right: 100x = 72.72¯¯¯¯¯

Now, subtract the original equation x = 0.72¯¯¯¯¯ from the second equation 100x = 72.72¯¯¯¯¯:

100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯

99x = 72

To simplify the fraction, divide both sides of the equation by 99:

99x / 99 = 72 / 99

x = 72/99

To simplify the fraction further, we can find the greatest common divisor (GCD) between 72 and 99, which is 9:

72/9 = 8
99/9 = 11

So, the simplified fraction is 8/11.

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

Answer 2

Which of the following is a rational number between 5 and 514?(1 point)
Responses

26−−√
start root 26 end root

517
5 Start Fraction 1 over 7 end fraction

525
5 Start Fraction 2 over 5 end fraction

513