Standard form: Practice Questions

Work out the value of the following expression, giving your answer in standard form:
\( (4 \times 10^7) \div (8 \times 10^{-2}) \)

Calculate \( ( 8.2 \times 10^6 ) - ( 3.1 \times 10^5 ) \). Give your answer in standard form.

A rectangular field has a length of \( 2.4 \times 10^3 \) meters and a width of \( 1.5 \times 10^2 \) meters. Calculate the area of the field in square meters, giving your answer in standard form.

Write the number 450,000 in standard form.

Calculate \( (2 \times 10^3) \times (4.5 \times 10^{-5}) \). Give your answer in standard form.

Write the number \( 0.00000000045 \) in standard form.

A square plot of land has an area of \( 6.4 \times 10^9 \) \( mm^2 \). Calculate the side length of the square, giving your answer in standard form.

A galaxy is approximately \( 9.46 \times 10^{17} \) km away. If light travels at \( 3 \times 10^5 \) km/s, how many seconds will it take for light from the galaxy to reach us? Give your answer in standard form to 3 significant figures.

(a) Work out \( ( 6.4 \times 10^{-3} ) \times ( 5 \times 10^{8} ) \). Give your answer in standard form.

(b) The volume of Earth is approximately \( 1.08 \times 10^{12} \) cubic kilometres. The volume of Mars is approximately \( 1.63 \times 10^{11} \) cubic kilometres. Calculate the difference between the volume of Earth and the volume of Mars, giving your answer in standard form.

The average distance from Earth to the Sun is \(1.5 \times 10^{11}\) metres. The speed of light is \(3.0 \times 10^8\) metres per second.

(a) Calculate the time, in seconds, for light to travel from the Sun to Earth. Give your answer in standard form.

(b) Express the Earth's distance from the Sun in gigametres (Gm), where 1 Gm = \(10^9\) metres.