Best Are Repeating Numbers Rational Gif

Best Are Repeating Numbers Rational
Gif. A repeating decimal is not considered to be a rational number it is a rational number. How is this a ratio if it shows this continuous pattern instead of being a finite it is clearly repeating, but when you apply it to a number, the answers are different:

9.2 rational and irrational numbers day 1 from image.slidesharecdn.com

If there were any repeating fractions for rational numbers in this base, we could manipulate the fraction around to get an equation with rational how can we prove that all rational numbers are either terminating decimal or repeating decimal numerals? This is clearly rational i'm giving you multiple examples of how this can be represented as the ratio as the ratio of two integers now what about repeating decimals well let's take maybe the most famous of the repeating decimals. Any #2# numbers that repeat go over #99# in a fraction.

If the number were something like, 111.010101., the repeating numbers would be 01 because in that case the first 0 is significant.

All terminating numbers are rational numbers as they can be written in the form of p/q easily. The content of the theorem is that any rational number, and only a rational number, has a repeating or terminating decimal expansion. I wrote a program that converts any number to a selected base, including rational numbers and negatives (unbiased of course). Any #2# numbers that repeat go over #99# in a fraction.