Squares, roots and powers
Squares, roots and powers

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Squares, roots and powers

3.1.1 Try some yourself

Activity 33

Express each of the following numbers in scientific notation.

  • (a) Light travels 9460 700 000 000 km in a year.

  • (b) The average distance from the centre of the Earth to the centre of the Moon is 384 400 km.

  • (c) Saturn is 1427 000 000 km from the Sun.

  • (d) The mass of the Earth is 5976 000 000 000 000 000 000 000 kg.

  • (e) The Mediterranean Sea has an area of 2504 000 km2.

  • (f) Annapurna 1 is 8075 m high.

  • (g) The diameter of the Sun is 1392 000 km. Use metres in your answer.

Answer

  • (a) Light travels at 9.4607 × 1012 km in a year.

  • (b) The distance from the centre of the Earth to the centre of the Moon is 3.844 × 105 km.

  • (c) Saturn is 1.427 × 109 km from the Sun.

  • (d) The mass of the Earth is 5.976 × 1024 kg.

  • (e) The Mediterranean Sea has an area of 2.504 × 106 km2.

  • (f) Annapurna 1 is 8.075 × 103 m high.

  • (g) 1392 000 km is 1392 000 000 m (multiplying by 1000). In scientific notation this is

  •   1.392 × 109 m.

  • (Alternatively: 1392 000 km is 1.392 × 106 km = 1.392 × 106 × 103 m = 1.392 × 109 m.)

Activity 34

The following numbers are given in scientific notation. Write each out as a single decimal number.

  • (a) Ben Nevis is 1.343 × 103 m high.

  • (b) Mercury is 5.8 × 107 km from the Sun.

  • (c) The distance from the Earth to the nearest star is about 4.3 × 1013 km.

  • (d) The Earth has a circumference of 4.0078 × 104 km at the equator.

  • (e) The span of the Golden Gate Bridge is 1.28 × 103 m.

  • (f) The Arctic Ocean has an area of 1.3986 × 107 km2.

Answer

  • (a) Ben Nevis is 1343 m high.

  • (b) Mercury is 58 000 000 km from the Sun.

  • (c) The distance from the Earth to the nearest star is about 43 000 000 000 000 km.

  • (d) The Earth has a circumference of 40 078 km at the equator.

  • (e) The span of the Golden Gate Bridge is 1280 m.

  • (f) The Arctic Ocean has an area of 13 986 000 km2.

Activity 35

Express each of the following in scientific notation.

  • (a) 0.53

  • (b) 0.0075

  • (c) 0.000 004

  • (d) 0.000 020 01

Answer

  • (a) 0.53 = 5.3 × 10−1

  • (b) 0.0075 = 7.5 × 10−3

  • (c) 0.000 004 = 4 × 10−6

  • (d) 0.000 020 01 = 2.001 × 10−5

Activity 36

Express each of the following in conventional decimal notation.

  • (a) 2.03 × 10−4

  • (b) 1.4 × 10−3

  • (c) 5.67 × 10−5

Answer

  • (a) 2.03 × 10−4 = 0.000 203

  • (b) 1.4 × 10−3 = 0.0014

  • (c) 5.67 × 10−5 = 0.000 0567

MU120_4M4

For further information, take a look at our frequently asked questions which may give you the support you need.

Have a question?
Free Courses

OpenLearn has over 800 free courses across all our subjects designed by our academic experts. From 1 to 100 hours, introductory to advanced, you can start learning at any time and all for free.