Number worksheet — GCSE Higher

1.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.

2.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

3.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

4.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

5.Work out the value of 2⁻²

6.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

7.Work out the value of 2⁻⁴

8.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

9.Write 60 as a product of its prime factors, using index notation.

10.Round 0.006482 to 2 significant figures.

11.Write down the symbol that makes this statement true: −2/3 ___ −5/6

12.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

13.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

14.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

15.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.