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.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

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

5.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

6.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

7.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

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

9.Write 0.35 as a fraction in its lowest terms.

10.Work out ⁴√16

11.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

12.Simplify √45.

13.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

14.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

15.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?