Number worksheet — GCSE Higher

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

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

3.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.

4.√700 lies between which two consecutive integers?

5.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

6.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

7.Work out (2/3)² + (1/2)². Give your answer as a fraction.

8.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.

9.Round 0.006482 to 2 significant figures.

10.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.

11.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?

12.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

13.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

14.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.

15.Write 0.875 as a fraction in its simplest form.