Stage 9 - Q1 - 2 marks
Write the fraction as an exact decimal.
Hint
Track remainders rather than copying a rounded calculator display.
Stage 9 - Q2 - 2 marks
Write the fraction as an exact decimal.
Hint
Track remainders rather than copying a rounded calculator display.
Stage 9 - Q3 - 2 marks
Write the fraction as an exact decimal.
Hint
Track remainders rather than copying a rounded calculator display.
Stage 9 - Q4 - 2 marks
Write the fraction as an exact decimal.
Hint
Track remainders rather than copying a rounded calculator display.
Stage 9 - Q5 - 3 marks
Express 23 minutes as an exact decimal number of hours. State whether it terminates.
Hint
Simplify the fraction of an hour before deciding its decimal type.
Stage 9 - Q6 - 3 marks
Express \(\frac{4}9\) in recurring notation, then find the exact decimal for twice this fraction.
Hint
Twice a recurring decimal may pass through 1.
Stage 9 - Q7 - 3 marks
A calculator displays 0.571429 for \(\frac{4}{7}\). Is that display exact? Give an exact notation.
Hint
A calculator screen can show only finitely many digits.
Stage 9 - Q8 - 4 marks
Compare \(1\) with its 2 d.p. display \(1.00\). Which is larger, or are they equal?
Hint
A rounded display is a different rational number unless the decimal terminates there.
Stage 9 - Q9 - 4 marks
Use long division or multiplication to show the exact decimal form of \(36/99\).
Hint
A two-digit period repeats after multiplying by 100.
Stage 9 - Q10 - 5 marks
Challenge: Prove exactly that \(0.\overline{36}+0.\overline{63}=1\). Explain why truncating both decimals first can give a different result.
Hint
Convert each two-digit repeating block into an exact fraction.