Stage 8 - Q1 - 2 marks
Write the fraction as an exact decimal.
Hint
Rewrite the denominator as 100.
Stage 8 - Q2 - 2 marks
Write the fraction as an exact decimal.
Hint
Multiply numerator and denominator by the same number.
Stage 8 - Q3 - 2 marks
Write the fraction as an exact decimal.
Hint
A denominator of 10000 will work.
Stage 8 - Q4 - 2 marks
Write 0.375 as a fraction in simplest form.
Hint
Start with a denominator of 1000.
Stage 8 - Q5 - 2 marks
Find the missing numerator.
Hint
Undo division by 40.
Stage 8 - Q6 - 2 marks
Write 2 hours 45 minutes as an exact decimal number of hours.
Hint
The minutes form a fraction of 60, not 100.
Stage 8 - Q7 - 2 marks
Without long division, explain whether \(\frac{21}{56}\) terminates.
Hint
Simplify before inspecting the denominator.
Stage 8 - Q8 - 3 marks
Find a fraction with denominator 24 whose decimal terminates, and one that recurs. Explain the difference.
Hint
Try numerators that cancel the factor 3.
Stage 8 - Q9 - 3 marks
A fraction has simplified denominator \(2^{3}\times 5^{2}\). What is the smallest power of 10 that can be its denominator?
Hint
Balance the numbers of factors 2 and 5.
Stage 8 - Q10 - 5 marks
Challenge: find all positive integers n less than 30 for which \(\frac{n}{30}\) has a terminating decimal. Explain why your list is complete.
Hint
Which prime factor prevents a simplified denominator from dividing a power of 10?