Convert 0.72727272 to a rational number in simplest form

Answer 1

To convert 0.72727272 to a rational number in simplest form, let's call it x and express it as an equation:

x = 0.72727272

To get rid of the repeating decimal, we can multiply x by a power of 10 that eliminates the repeating part. In this case, 10 is enough to eliminate the repeating part. Multiply both sides of the equation by 10:

10x = 7.2727272

Next, subtract the original equation from the equation multiplied by 10:

10x - x = 7.2727272 - 0.72727272
9x = 6.54545448

Simplifying the equation:

x = 6.54545448 / 9

To further simplify, we can divide both the numerator and denominator by their greatest common divisor, which is 1:

x = 6.54545448 ÷ 9
x ≈ 0.72727272

Therefore, 0.72727272 as a rational number in simplest form is approximately 0.72727272.