Squares, roots and powers
Squares, roots and powers

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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

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