16. The distance between two planets is 240 megametres $$ \left(1 \mathrm{Mm}=10^{6} \mathrm{~m}\right) $$. (i) Express this distance in metres. Give your answer in standard form. A rocket travels a distance of one metre in 8000 nanoseconds (ns) and $$ 1 \mathrm{~ns}=10^{-9} \mathrm{~s} $$. (ii) How long does the rocket take to travel from one planet to the other? Give your answer in seconds.

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**(i) Converting 240 megametres to metres in standard form**

- Given that $$1 \, \text{Mm} = 10^6 \, \text{m}$$, we have:
  $$
  240 \, \text{Mm} = 240 \times 10^6 \, \text{m}
  $$
- Expressing $$240 \times 10^6$$ in standard form:
  $$
  240 \times 10^6 = 2.4 \times 10^8 \, \text{m}
  $$

**(ii) Calculating the time the rocket takes**

- The rocket travels $$1 \, \text{m}$$ in $$8000 \, \text{ns}$$, and given $$1 \, \text{ns} = 10^{-9} \, \text{s}$$, the time for $$1 \, \text{m}$$ is:
  $$
  8000 \, \text{ns} = 8000 \times 10^{-9} \, \text{s} = 8 \times 10^{-6} \, \text{s}
  $$
- To find the total time to travel $$2.4 \times 10^8 \, \text{m}$$:
  $$
  \text{Time} = \text{distance} \times \text{time per metre} = (2.4 \times 10^8 \, \text{m}) \times (8 \times 10^{-6} \, \text{s/m})
  $$
- Multiplying the numbers:
  $$
  2.4 \times 8 = 19.2
  $$
- Combining the powers of ten:
  $$
  10^8 \times 10^{-6} = 10^{2}
  $$
- Therefore:
  $$
  \text{Time} = 19.2 \times 10^2 \, \text{s} = 1.92 \times 10^3 \, \text{s}
  $$

**Answer:**

- (i) $$2.4 \times 10^8 \, \text{m}$$
- (ii) $$1.92 \times 10^3 \, \text{s}$$
**(i) 2.4 × 10⁸ meters** **(ii) 1.92 × 10³ seconds**

The distance between two planets is
240 megametres .
(i) Express this distance in metres. Give your
answer in standard form.
A rocket travels a distance of one metre in
8000 nanoseconds (ns) and .
(ii) How long does the rocket take to travel from
one planet to the other? Give your answer in
seconds.

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