These three notations describe the same amount in different clothes:

• Fraction → Decimal: divide the numerator by the denominator. $\dfrac{5}{8} = 5 \div 8 = 0.625$
• Decimal → Percentage: multiply by $100$. $0.625 \times 100 = 62.5\%$
• Percentage → Fraction: write over $100$ and simplify. $62.5\% = \dfrac{625}{1000} = \dfrac{5}{8}$

Core tier note: you're expected to simplify fractions fully, but you will never be asked to convert a recurring decimal to a fraction (or back) — that's Extended-only.

Convert the mixed number to an improper fraction first, then divide.

Example: write $4\frac{3}{8}$ as a decimal and a percentage.

1. $4\frac{3}{8} = \dfrac{(4 \times 8) + 3}{8} = \dfrac{35}{8}$
2. Divide: $35 \div 8 = 4.375$
3. Multiply by $100$: $4.375 \times 100 = 437.5\%$

A fraction in its simplest form gives a terminating decimal only if the denominator's prime factors are made up exclusively of $2$s and/or $5$s — because our number system is base $10 = 2\times 5$. Any other prime factor in the denominator (like $3$, $7$, or $11$) forces the decimal to recur.

• $\dfrac{3}{8}$: denominator $8 = 2^3$ (only 2s) → terminates: $0.375$.
• $\dfrac{1}{3}$: denominator $3$ (not 2 or 5) → recurs forever: $0.333\ldots$
• $\dfrac{7}{20}$: denominator $20 = 2^2 \times 5$ (only 2s and 5s) → terminates: $0.35$.

Core tier note: you are never asked to write a recurring decimal using dot notation, or to convert one back into a fraction — you would only be expected to round it, e.g. give $0.333\ldots$ as $0.33$ to 2 d.p.

Convert everything to decimals (to 3 decimal places is usually safe), order the decimals, then write your final answer using the original notation given in the question.

Write these in order of size, smallest first: $\dfrac{3}{5}, \quad 58\%, \quad 0.615, \quad \dfrac{11}{20}$.

1. Convert each to a decimal: $\frac{3}{5} = 0.600$, $58\% = 0.580$, $0.615 = 0.615$, $\frac{11}{20} = 0.550$.
2. Order the decimals: $0.550 < 0.580 < 0.600 < 0.615$.
3. Restate using the original forms:

• Leaving the final answer as decimals instead of restating it in the original fractions/percentages — the decimals were only a working tool, and the mark scheme wants the original forms back.
• Not simplifying a fraction fully, e.g. leaving $\frac{6}{8}$ instead of dividing by the HCF to get $\frac{3}{4}$.
• Losing track of the decimal point when converting a mixed number — always convert the fractional part on its own before adding it to the whole number.