① Decimal → Fraction 2nd Level
1 or 2 decimal places. Write over 10 or 100 then simplify. e.g. \(0.8 = \tfrac{8}{10} = \tfrac{4}{5}\)
② Decimal → Fraction 3rd Level
3 or 4 decimal places including small decimals like \(0.004\) or \(0.625\). Write over 1000 or 10000 then simplify.
③ Fraction → Decimal 2nd Level
Scale the denominator to 10 or 100. e.g. \(\tfrac{2}{5} = \tfrac{4}{10} = 0.4\) or \(\tfrac{3}{20} = \tfrac{15}{100} = 0.15\)
④ Fraction → Decimal 3rd Level
More complex fractions requiring simplification first, then scaling. e.g. \(\tfrac{32}{80} \to \tfrac{2}{5} \to 0.4\)
⑤ Fraction → Percentage 2nd Level
Scale denominator to 100. e.g. \(\tfrac{2}{5} = \tfrac{40}{100} = 40\%\)
⑥ Fraction → Percentage 3rd Level
Simplify first, then scale to 100. e.g. \(\tfrac{32}{80} = \tfrac{8}{20} = \tfrac{40}{100} = 40\%\)
⑦ Decimal → Percentage & Percentage → Decimal 2nd Level
\(\times 100\) to go decimal → %, \(\div 100\) to go % → decimal.
Key methods
Decimal → Fraction: count decimal places, write over 10/100/1000/10000, then simplify by HCF.
Fraction → Decimal: find what multiplies denominator to give 10 or 100, apply same to numerator.
Fraction → %: scale denominator to 100 — the numerator is the percentage.
Decimal ↔ %: multiply by 100 (decimal → %), divide by 100 (% → decimal).