Number worksheet — GCSE Higher

1.Write 5/6 as a decimal, showing clearly which digit recurs.

2.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

3.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

4.Simplify x⁶ ÷ x²

5.Work out the reciprocal of (2 + 3)

6.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

7.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

8.Find the missing number: ▢ ÷ 15 = 24

9.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

10.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

11.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

12.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

13.Work out ⁴√16

14.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

15.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.