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 Round each number to 1 significant figure to estimate 612 × 0.048.
Show worked solution
612 → 600 and 0.048 → 0.05. 600 × 0.05 = 600 × 5 ÷ 100 = 30. 300 rounds 0.048 to 0.5; 3 rounds it to 0.005; 3000 ignores the decimal point.
2 Round each front number to 1 significant figure to estimate (3.9 × 105) × (2.2 × 10−8).
Show worked solution
4 × 2 = 8 and 5 + (−8) = −3: 8 × 10−3.
3 Round each number to 1 significant figure to estimate 7 890 ÷ 0.019. Give the estimate as an ordinary number.
Show worked solution
8000 ÷ 0.02 = 8000 × 50 = 400 000.
Level 2 · Core
4 Round each front number to 1 significant figure to estimate (6.2 × 107) × (4.9 × 10−3) ÷ (1.8 × 102).
Show worked solution
6 × 5 ÷ 2 = 15 and 7 + (−3) − 2 = 2, so 15 × 102 = 1.5 × 103. 1.5 × 102 forgets to add 1 to the power when fixing the front; 1.5 × 107 adds the divisor's power; 6 × 107 multiplies by the divisor.
5 A hair grows about 4.2 × 10−9 m every second, and there are 86 400 seconds in a day. Round each number to 1 significant figure to estimate how far it grows in one day, in metres.
Show worked solution
86 400 → 9 × 104 and 4.2 → 4. 4 × 9 = 36 and −9 + 4 = −5: 36 × 10−5 = 3.6 × 10−4 m, about a third of a millimetre.
6 A bacterium is 2.3 × 10−6 m long. Round to 1 significant figure to estimate how many, placed end to end, would stretch 1 cm.
Show worked solution
1 cm = 10−2 m. 10−2 ÷ (2 × 10−6) = 0.5 × 104 = 5000.
Level 3 · Challenge
7 Each estimate below rounds every number to 1 significant figure first.
1 0.000 0716 ≈ 7 × 10−5
2 (8.7 × 103) × (5.2 × 10−7) ≈ 4.5 × 10−4
3 (3.4 × 106) ÷ (5.9 × 10−2) ≈ 5 × 107
Which statements are correct?
1 0.000 0716 ≈ 7 × 10−5
2 (8.7 × 103) × (5.2 × 10−7) ≈ 4.5 × 10−4
3 (3.4 × 106) ÷ (5.9 × 10−2) ≈ 5 × 107
Which statements are correct?
Show worked solution
0.000 0716 = 7.16 × 10−5, which rounds to 7 × 10−5 (1 ✓). 9 × 5 = 45 and 3 + (−7) = −4, so 45 × 10−4 = 4.5 × 10−3, not 10−4 (2 ✗). 3 ÷ 6 = 0.5 and 6 − (−2) = 8, so 0.5 × 108 = 5 × 107 (3 ✓). 1 and 3.
8 Round each front number to 1 significant figure, then estimate (4.1 × 10−3)2 × (3.1 × 108). Do not round the result.
Show worked solution
(4 × 10−3)2 = 16 × 10−6. Then 16 × 3 = 48 and −6 + 8 = 2: 48 × 102 = 4.8 × 103.
9 A calculator shows 0.0081 × 0.0029 ÷ 0.000 62 = 3.789, but the decimal point is in the wrong place. Round each number to 1 significant figure. What is your estimate of the true value?
Show worked solution
8 × 3 ÷ 6 = 4 and −3 + (−3) − (−4) = −2, so the estimate is 4 × 10−2 = 0.04. The true value is about 0.0379, so 3.789 is 100 times too big.