Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Work out 3.6 × 104 + 4 × 103. Which is the answer in scientific notation?
Show worked solution
36 000 + 4 000 = 40 000 = 4 × 104.
2 Round 0.000 905 to 2 significant figures, then write it in scientific notation.
Show worked solution
2 s.f.: 0.000 91, which is 9.1 × 10−4.
3 How many significant figures does 0.004 050 have?
Show worked solution
4, 0, 5, 0 — the leading zeros do not count: 4 significant figures.
Level 2 · Core
4 (2.5 × 106) ÷ (5 × 10−2) = ?
Show worked solution
2.5 ÷ 5 = 0.5 and 6 − (−2) = 8, giving 0.5 × 108 = 5 × 107.
5 Round 3 816 450 to 3 significant figures, then write it in scientific notation.
Show worked solution
3 s.f.: 3 820 000 = 3.82 × 106.
6 A sheet of paper is 8 × 10−2 mm thick. How many sheets make a stack 4 cm high?
Show worked solution
40 ÷ 0.08 = 500 sheets.
Level 3 · Challenge
7 Light travels at 3 × 108 m/s, and the Sun is 1.5 × 1011 m from Earth.
1 Sunlight takes 500 seconds to reach Earth.
2 That is less than 10 minutes.
3 In one hour light travels 1.08 × 1011 m.
Which statements are correct?
1 Sunlight takes 500 seconds to reach Earth.
2 That is less than 10 minutes.
3 In one hour light travels 1.08 × 1011 m.
Which statements are correct?
Show worked solution
1.5 × 1011 ÷ 3 × 108 = 0.5 × 103 = 500 s (1 ✓), which is 8 min 20 s (2 ✓). 3 × 108 × 3600 = 1.08 × 1012, not 1011 (3 ✗). 1 and 2.
8 A grain of sand has a mass of 2 × 10−5 kg. How many grains are there in 1 kg of sand? Give the answer in scientific notation.
Show worked solution
0.5 × 105 = 5 × 104 grains.
9 Work out (6 × 105) × (5 × 10−3) and give the answer as an ordinary number.
Show worked solution
30 × 102 = 3000.