Move freely between fractions, decimals and percentages
Fraction → decimal: divide. Decimal → percentage: . Percentage → fraction: put over and simplify.
Recurring decimal → fraction needs algebra
Let equal the decimal, multiply by a power of so the recurring tails line up, subtract to remove the recurring part, then solve for and simplify.
Drawn from real examiner reports.
Jumping to the calculator with no working
On the non-calculator paper, leaping to the final fraction (e.g. straight to ) with no improper-fraction or cancelling step shown loses method marks — and can hide errors.
Not using algebra for a recurring decimal
When told to "use algebra to show" a recurring decimal equals a fraction, a non-algebraic answer scores at most 1 mark.
Subtracting the wrong multiples of x
Choosing and (or other mismatched powers) so the recurring tails do NOT cancel — you must pick powers whose decimal parts are identical before subtracting.
Always give the fraction in its simplest form
After the algebra, cancel down (e.g. ) — an un-simplified fraction can cost the final mark.
Convert a fraction to a decimal — how?
Write as a decimal and as a percentage.
