Question

1.27272727 is a rational number​

Answer 1

Answer:

One common way of writing rational numbers is as repeating decimals. Remember that when we write a decimal with a bar over some of its numbers, like 1.27, what we mean is that those numbers are repeated infinitely:

1.27=1.27272727...

You can use algebra to convert any repeating decimal into a fraction. For example, you can convert 1.27 to a fraction as follows:

x=1.27x=1.2727pulling out the first repetition100x=127.27multiplying both sides by 100100x−x=127.27−xsubtractingxfrom both sides...99x=127.27−1.27...and using the fact thatx=1.27...99x=126...to make the repeated part cancel out99x99=12699x=1411

We multiplied by 100=102 in order to shift the repeating decimal over by 2 decimal places, because there were 2 repeated digits. In general, if there are n repeated digits, then we multiply by 10n to shift the repeating decimal over by n decimal places.