From a Recurring Decimal to a Fraction

Zero point seven seven seven… goes on for ever. Can it be a fraction? Multiply by ten, line the endless tails up, subtract — and the tail vanishes: 9x = 7. Then periods of two digits, periods that start later, the rational numbers, and why √2 and π are not fractions. Timestamps (measured on the final): 0:00 — Endless digits, a fraction? 0:24 — The Method 0:58 — The tails cancel 1:57 — When the period starts later 2:48 — Rational numbers 4:01 — Irrational numbers exist 4:36 — Your turn 5:09 — Let's Remember! 🎓 Free interactive lesson: https://commeunjeu.org/cours/ib-myp-3... 📱 Android: https://play.google.com/store/apps/de... 📱 iPhone: https://commeunjeu.org/mobile/ 🎵 Music: "Ever Mindful" by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 4.0 http://creativecommons.org/licenses/b...