Number worksheet — GCSE Higher

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

2.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.

3.Write 7/12 as a decimal, showing clearly which digit is recurring.

4.Work out the value of 2⁻⁴

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.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

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

8.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

9.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

10.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

11.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

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

13.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

14.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

15.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.