Number worksheet — GCSE Higher

1.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

2.Write 0.36 as a fraction in its simplest form.

3.Work out √25 + 4² − 12 ÷ 3

4.Find the missing number: 17 × ▢ = 391

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 decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

7.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

8.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

9.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.

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

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

12.Work out √3 × √12, giving your answer as an integer.

13.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?

14.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.