Number worksheet — GCSE Higher

1.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

2.Work out the value of 2⁻²

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

4.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

5.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

6.Last year a company made a profit of £5,200,000. Write this amount in standard form.

7.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

8.Work out √225 ÷ 3.

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

10.Simplify (y³)⁴, giving your answer as a single power of y.

11.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

12.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

13.√700 lies between which two consecutive integers?

14.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

15.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.