Scientific notation

Express the following integers and terminating decimals in standard form:

1. a) $450\,000\,000$
2. b) $32\,500$
3. c) $8\,400\,000\,000\,000$

Express the following small decimal numbers in standard form:

1. a) $0,0000045$
2. b) $0,00000000128$
3. c) $0,003$

Write out in full the following numbers given in standard form:

1. a) $3,14 \cdot 10^6$
2. b) $8,05 \cdot 10^9$
3. c) $1,002 \cdot 10^4$

Write the following numbers given in standard form in decimal form:

1. a) $5,2 \cdot 10^{-5}$
2. b) $1,07 \cdot 10^{-8}$
3. c) $9,9 \cdot 10^{-3}$

Order the following numbers from smallest to largest, having first expressed them in standard form (with a single non-zero digit before the decimal point):

$A = 0,0034 \cdot 10^8$

$B = 450 \cdot 10^3$

$C = 3,2 \cdot 10^5$

$D = 0,05 \cdot 10^7$

Carry out the following multiplications and give the answer in standard form:

1. a) $(3 \cdot 10^4) \cdot (2 \cdot 10^5)$
2. b) $(4 \cdot 10^{-3}) \cdot (2 \cdot 10^8)$

The mean distance from the Earth to the Sun is about $149\,600\,000$ km and the speed of light in a vacuum is approximately $300\,000$ km/s. Express both quantities in standard form and calculate how many seconds it takes for light from the Sun to reach the Earth.

The law of universal gravitation states that the gravitational force between two masses $m_1$ and $m_2$ separated by a distance $d$ is $F = G \cdot \frac{m_1 \cdot m_2}{d^2}$, where $G = 6,67 \cdot 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2$. Calculate the force of attraction between the Earth ($m_1 = 5,97 \cdot 10^{24}$ kg) and the Moon ($m_2 = 7,35 \cdot 10^{22}$ kg), given that the mean distance between their centres is $3,84 \cdot 10^8$ m. Give the answer in standard form to three significant figures.