Number worksheet — GCSE Higher

1.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

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

3.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

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

5.Work out (5 + 2) × 3²

6.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.

7.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

8.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

9.Write 0.06 as a fraction in its simplest form.

10.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

12.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

13.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

14.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

15.A country has an area of 25,000,000 hectares. Write this area in standard form.