← GCSE Mathematics

N10 Fractions and decimals, recurring decimals

Currently Developing · last touched 2026-10-19

Still to see x = ... as its own line before the simplified fraction (recurring decimal to fraction).

Every change

WhenChangeEvidenceSession
2026-10-20Developing → Developing19 Oct: recurring decimals re-taught, say-back right in her words; independent 5/6 -> 0.8 with dot on the 3 and 3/11 -> 0.2 7 with dots, 2/2, no hints; used '...' before dots were required.session 119
2026-10-09Developing → Developing9 Oct mixed set, non-calc, no cue, a new decimal: show that 0.7272... = 8/11 -> 'x = 0.7272r, x*100 = 100x = 72.7272r, 100x - x = 99x = 72, 72/99 = 8/11' in 2 min, unaided. 100x and 99x lines both written; 'x = 72/99' not written as its own line. Second uncued full chain (first 2 Oct); the 7 Oct timed paper lacked the 100x line (2/3). Session 90. Retrieval outcome: correct.standalone
2026-10-07Developing → DevelopingExam practice 7 Oct (test #7, attempt #15, timed) Q7, no cue: show 0.3636... = 4/11, she wrote 'x*100 = 100x, 100x - x = 99x = 36, 36/99 = 4/11'; 2/3. Subtraction and simplification right; the line giving 100x as a decimal and 'x =' not written. Marking only: no status change. Retrieval outcome: retry.standalone
2026-10-02Developing → DevelopingMixed set Q6 unaided, no cue: 'x = 0.5454r, x * 100 = 100x, 100x = 54.5454r, 100x - x = 99x = 54, 54/99 = 6/11' — 100x and 99x lines both written; 'x = 54/99' not written as its own line.session 65
2026-09-29Developing → Developing29 Sep starter, non-calc, show that 0.8181… = 9/11 asked as 'write what 100x equals first' → 'x = 0.81, x*100 = 100x = 81.81r, 100x - x = 99x = 81, 81/99 = 9/11'. Full chain including the 100x line, first time; cue was in the question. x written without a recurring mark.session 56
2026-09-28Developing → Developing28 Sep starter, non-calc, unlabelled show-that 0.6363… = 7/11 → 'x = 0.63r, x*100, 100x - x = 99x = 63, 63/99 = 7/11'. Correct; 99x = 63 written for the first time; 100x = 63.6363… line still missing.session 49
2026-09-25Developing → Developing25 Sep starter, unlabelled show-that 0.4545… = 5/11 (non-calc) → 'x = 0.45r, 100x - x = 45, 45/99 = 5/11'. Correct, lines before the answer, no false statement (unlike 24 Sep), but the 100x = 45.4545… line and '99x =' still missing.session 46
2026-09-24Developing → Developing24 Sep starter, unlabelled show-that 0.2727… = 3/11 → 'x = 0.27r, 100x - x = 99x = 27/99 = 3/11'. Lines came first (unlike 22 Sep's bare 4/11) but 100x = 27.27… omitted and 99x = 27 miswritten as 99x = 27/99.session 43
2026-09-22Developing → Developing22 Sep starter, labelled method marks only: 0.3636… → bare '4/11' correct; on request wrote 100x = 36.3636, 100x − x = 99x, 36/99 = 4/11, omitting 99x = 36. Third correct recurring decimal, third time the method came only when asked.session 38
2026-09-15Developing → Developing15 Sep starter, non-calc: 0.27 recurring → 3/11 correct. First working offered was "0.27 × 11 = 3/11" (not a method); when asked how she got it, produced the full method unprompted: x = 0.2727…, 100x = 27.2727…, subtract, 99x = 27, 27/99 = 3/11. Wrote the subtraction as x − 100x. Second correct recurring decimal (2 Sep 0.444… → 4/9), first two-digit repeat.session 24
2026-09-03Developing → Developing2 Sep starter: 0.444… → 4/9 correct. First recurring-decimal question asked since it was taught on 18 Aug, so the loose end now has one correct independent answer. One question only, so no promotion.session 3

In papers

AttemptPaperQMarksNote
Exam practice — week 41 — GCSE Mathematics sectionexam-skills #772/3M0 (first): the line 100x = 36.36… is never written — 'x*100 = 100x' carries no decimal, so the step that produces 36 is not shown. M1: '100x − x = 99x = 36', subtraction shown. A1: 36/99 = 4/11 seen. The alternative reading (first M implied by 99x = 36, A0 for an incomplete show-that with no 'x =') gives the same 2. No cue on the paper; 1 min on focus.

Materials

Corbettmaths: Recurring Decimals to Fractions Video
Models the algebraic (multiply-by-10^n then subtract) method.
video
Corbettmaths: Recurring Decimals Practice Questions
Worksheet converting recurring decimals to fractions.
practice
Maths Genie: Recurring Decimals into Fractions booklet
Exam-style question booklet as a second practice set.
practice