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Standard Form Multiplication

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Standard Form Multiplication

Multiply the numbers in front, add the powers of 10, then rewrite the result so the first number is at least 1 but less than 10. Show your working.

Core calculations

1.Work out (4 × 10⁵) × (3 × 10²). Give your answer in standard form.

2.Calculate (7 × 10³) × (2 × 10⁴), writing your answer in standard form.

3.Find (6 × 10⁻²) × (5 × 10⁶) in standard form.

4.Work out (3.5 × 10⁴) × (1.4 × 10³). Express the result in standard form.

5.Which line correctly evaluates (9 × 10²) × (6 × 10³) and gives the result in standard form?

15 × 10⁵ = 1.5 × 10⁶
54 × 10⁵ = 5.4 × 10⁶
54 × 10⁶ = 5.4 × 10⁷
15 × 10⁶ = 1.5 × 10⁷

Applications

6.A tiny sensor has a mass of 2.4 × 10⁻⁵ kg. Find the combined mass of 300 identical sensors. Give your answer in standard form.

7.A radio signal travels at 2.8 × 10⁸ metres per second. How far does it travel in 4.5 × 10² seconds? Give the distance in metres and in standard form.

8.A rectangular microchip is 8.0 × 10⁻⁴ metres long and 2.5 × 10⁻⁵ metres wide. Calculate its area in square metres, giving your answer in standard form.

Challenge

9.Evaluate (5 × 10²) × (4 × 10⁻³) × (7 × 10⁵). Write your answer in standard form.

10.A data centre carries out 3.2 × 10⁸ operations each second. Each operation uses 2.5 × 10⁻¹⁰ joules. How much energy is used in 6.0 × 10³ seconds? Give your answer in joules and in standard form.

11.Explain why the powers of 10 are combined when multiplying numbers written in standard form.