Number worksheet — GCSE Higher

1.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

2.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

3.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

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

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

6.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

7.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.

8.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

9.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

10.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

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.Work out (−3) × 4 + 2 × (−5)

13.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

14.Write ∛(x²) as a single power of x.

15.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.