Mathematics Class 9
The World of Numbers
Which fractions repeat, why some lengths are not fractions, and how to read a decimal.
17 lessons · ~125 min total
Track progress — 0 of 17 lessons read 0%
Lessons in this topic
- 0 Start here Rational numbers, decimals that stop or repeat, lengths no fraction reaches, and the square root spiral. · 3 min You are here
- 1 Every number so far is one integer over another Whole numbers, negatives, mixed numbers, percentages and stopping decimals all fit one shape. · 7 min
- 2 There is always another one in the gap Halfway between two fractions is another fraction. So no fraction has a next-door neighbour. · 7 min
- 3 Which fractions stop, and what decides it Cut the fraction down first. If its bottom number has only 2s and 5s, the decimal stops. · 8 min
- 4 A block that repeats is the number written out When a remainder comes back, every digit after it comes back too. That block repeats. · 8 min
- 5 Turning a repeating decimal back into a fraction Two lines with the same repeating tail, taken away, leave a whole number. That gives the fraction. · 8 min
- 6 Checkpoint: fractions and the decimals they make A graded check on the first five ideas — one shape underneath, no next-door neighbour, which decimals stop, why a block repeats, and the road back. · 6 min
- 7 A length you can draw and cannot write The diagonal of a one-unit square squares to 2. No fraction squares to exactly 2. · 8 min
- 8 The argument that no fraction can do it Suppose a fraction in lowest terms squares to 2. Then p and q are both even, which is a clash. · 11 min
- 9 A spiral built one right triangle at a time Stand a new leg of 1 on each longest side. The squares of those sides go up by 1. · 8 min
- 10 Squeezing it between two fractions Square the ends of a gap. Each new digit narrows the gap that holds a root. · 8 min
- 11 Checkpoint: the numbers that are not fractions A graded check on the second four ideas — a length whose square is 2, the argument that rules out every fraction, the spiral, and the squeeze. · 6 min
- 12 One number can have two decimal names The decimal 0.999… with endless 9s is exactly 1. · 8 min
- 13 A block that turns round: 142857 Times 1 to 6, 142857 gives the same six digits, shifted. · 8 min
- 14 The decimal tells you if a number is rational Stops or repeats means rational. Never ends and never repeats means irrational. · 8 min
- 15 The big picture Twelve ideas, tied back together. · 4 min
- 16 Track quiz Cheat-sheet table plus a reveal quiz — one question per idea. · 9 min
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