Number: approximation, error intervals and calculators – Year 9 maths test to download as PDF

Round each number as instructed.

1. \(5.0764\) to 2 decimal places (1 mark)
2. \(5.0764\) to 3 significant figures (1 mark)
3. \(0.007382\) to 2 significant figures (1 mark)
4. \(36\,450\) to 1 significant figure (1 mark)

Estimate \(\dfrac{6.9\times4.1}{0.52}\).

1. Round each number to 1 significant figure and work out the estimate. (2 marks)
2. Use a calculator to find the exact answer to 3 significant figures. (1 mark)
3. Is your estimate an over-estimate or under-estimate? (1 mark)

Write down the error interval for each.

1. \(l=8.6\) cm to 1 decimal place (2 marks)
2. \(m=450\) g to the nearest 10 g (1 mark)
3. \(n=3000\) to 1 significant figure (1 mark)

Fatima cycles 60 km, to the nearest kilometre, in 2.5 hours, to the nearest 0.1 hour. Speed \(=\) distance \(\div\) time.

1. Write the bounds for the distance and the time. (2 marks)
2. Find the upper and lower bounds of her speed to 1 decimal place. (2 marks)

Here are five numbers: \(\sqrt{49}\), \(\sqrt{7}\), \(0.5\), \(\pi\), \(\dfrac49\).

1. Write down the irrational numbers. (2 marks)
2. Show that \(0.5\) is rational. (1 mark)
3. Explain why \(\sqrt{49}\) is not irrational. (1 mark)