Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Write 3/5 as a decimal.
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3/5 = 6/10 (×2 top and bottom) = 0.6. Or divide: 3 ÷ 5 = 0.6.
2 Write 0.8 as a fraction in simplest form.
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0.8 = 8/10; divide top and bottom by 2: 4/5.
3 Does 4/9 terminate or recur?
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9 = 3 × 3 — a prime other than 2 or 5 — so 4/9 recurs: 4/9 = 0.4̇.
Level 2 · Core
4 Write 7/8 as a decimal.
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7 ÷ 8 by short division: 8 into 70 = 8 r 6; 8 into 60 = 7 r 4; 8 into 40 = 5 r 0. So 0.875.
5 Write 0.36 as a fraction in simplest form.
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0.36 = 36/100; divide top and bottom by 4: 9/25.
6 Does 9/40 terminate or recur?
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40 = 2 × 2 × 2 × 5 — only 2s and 5s — so it terminates (9/40 = 0.225).
Level 3 · Challenge
7 Write 0.7̇ (0.777…) as a fraction.
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Let x = 0.777…; then 10x = 7.777…. Subtracting: 9x = 7, so x = 7/9.
8 Write 0.4̇5̇ (0.4545…) as a fraction in simplest form.
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Two-digit block → ×100: x = 0.4545…, 100x = 45.4545…. Subtract: 99x = 45, x = 45/99 = 5/11.
9 Is 3.1416 rational or irrational?
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It terminates (four decimal places), so it is rational: 31416/10000. It is an approximation of π — but π itself is a different, irrational number.