Number worksheet — GCSE Higher

1.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

2.Work out √144 − 2 × 3 + √25

3.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

4.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

5.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

6.4ˣ = 64. Work out the value of x.

7.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

9.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

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

11.Work out 35% of 180.

12.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

13.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.

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

15.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?