2³ works out to 8 and 10⁴ works out to 10,000, so this Year 8 sheet opens by evaluating the basic indices. The key records 300 and 0.01 as later answers, and 4.2 × 10² as a standard form result.
Key Takeaways
2³ = 8 (Q1).
10⁴ = 10,000 (Q2).
Q6 records 4.2 × 10² in standard form.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Work out 2³.
(a) 6(b) 8(c) 9(d) 4
2.Work out 10⁴.
(a) 1,000(b) 100(c) 10,000(d) 100,000
3.Work out 5⁰.
(a) 0(b) 1(c) 5(d) 10
4.Write 3 × 10² as an ordinary number.
(a) 300(b) 30(c) 3,000(d) 310
5.Work out 10⁻².
(a) 0.1(b) 0.01(c) 100(d) -100
6.Which of these numbers is written in standard form?
(a) 0.5 × 10³(b) 4.2 × 10²(c) 42 × 10(d) 420
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Work out 2⁴.
8.Write 7 × 10³ as an ordinary number.
9.Write 600,000 in standard form.
10.Work out 3² × 3³, leaving your answer as a power of 3.
11.Write 0.0004 in standard form.
12.Work out 5³.
13.Write 8 × 10⁻³ as an ordinary number.
14.Work out (2²)³, leaving your answer as a power of 2.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.Light travels at about 3 × 10⁸ metres per second. How far does it travel in 10 seconds?
16.A dish contains 2³ bacteria. After 2 hours the number of bacteria is multiplied by 2². Find the total number of bacteria.
17.The population of a city is 5.4 × 10⁶. Write this as an ordinary number.
18.A computer can do 10⁷ calculations in one second. How many calculations can it do in 10 seconds? Give your answer as a power of 10.
19.The mass of one grain of sand is about 5 × 10⁻⁴ grams. Find the mass of 1,000 grains of sand.
20.A sheet of paper is 7 × 10⁻² mm thick. Find the total thickness of a pile of 10 sheets, giving your answer in millimetres.
Answer Key
1. b) 8
2. c) 10,000
3. b) 1
4. a) 300
5. b) 0.01
6. b) 4.2 × 10²
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
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14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is 2³?
8, option (b) in this worksheet (Q1).
What is 10⁴?
10,000, option (c) in this worksheet (Q2).
How is 420 written in standard form?
4.2 × 10², option (b) in this worksheet (Q6).
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