Number worksheet — GCSE Higher

1.Write 90 as a product of its prime factors.

2.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

3.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

4.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

5.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

6.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

7.Round 592.5 to the nearest 10.

8.Work out the value of (√5)⁴

9.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

10.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

11.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

12.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

14.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

15.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.