Stage 8 - Q1 - 2 marks
Write the fraction as an exact decimal.
Hint
Use the repeating pattern for ninths.
Stage 8 - Q2 - 2 marks
Write the fraction as an exact decimal.
Hint
Continue division until the same remainder appears.
Stage 8 - Q3 - 2 marks
Write the fraction as an exact decimal.
Hint
Some digits before the repeating block do not repeat.
Stage 8 - Q4 - 2 marks
Write the first seven decimal places of the number shown.
Hint
Identify which digits are inside the bar.
Stage 8 - Q5 - 2 marks
Write 3 hours 35 minutes as an exact recurring decimal number of hours.
Hint
Convert the minutes as a fraction of an hour.
Stage 8 - Q6 - 2 marks
A calculator shows 0.777778 for \(\frac{7}{9}\). Explain the final 8.
Hint
The calculator has a limited number of displayed digits.
Stage 8 - Q7 - 2 marks
Decide which of the two decimals is larger. Explain.
Hint
Write enough decimal places to find the first difference.
Stage 8 - Q8 - 2 marks
The digits of \(\frac{2}{7}\) repeat as 285714. What is the 100th digit after the decimal point?
Hint
Find the position inside the six-digit block.
Stage 8 - Q9 - 3 marks
Explain why \(\frac{6}{21}\) and \(\frac{2}{7}\) have the same recurring block, and find the 20th digit.
Hint
Simplify, then use the length of the repeating cycle.
Stage 8 - Q10 - 5 marks
Challenge: among \(\frac{n}{12}\) for integers \(1\le n\le 11\), which decimals terminate and which recur? Prove your classification.
Hint
Decide exactly when the factor 3 cancels from the denominator.