Number worksheet — GCSE Higher

1.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

2.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

3.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.

4.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.

5.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

6.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

7.Write 200 as a product of its prime factors, using index notation.

8.Work out √225 ÷ 3.

9.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.

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

11.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

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

13.Work out 5⁰ + 5¹ + 5²

14.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

15.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.