Notes & theory for this topic

Units

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1. Calculate the following conversions, giving your answers to 3 significant figures. Remember to add the units.
  1. How many kg are there in 7 lb?
    Show answer
    1 lb = 0.4536 kg
    7 lb = 3.18 kg
  2. How many mm are there in 4 in?
    Show answer
    1 in = 25.4 mm
    4 in = 102 mm
  3. How many km are there in 7 mile?
    Show answer
    1 mile = 1.6093 km
    7 mile = 11.3 km
  4. How many l are there in 6 pt?
    Show answer
    1 pt = 0.5683 l
    6 pt = 3.41 l
2. Calculate the following conversions, giving your answers to 3 significant figures. Remember to add the units.
  1. How many mile are there in 13 km?
    Show answer
    1 km = 0.6214 mile
    13 km = 8.08 mile
  2. How many lb are there in 2 kg?
    Show answer
    1 kg = 2.2046 lb
    2 kg = 4.41 lb
  3. How many gal are there in 120 l?
    Show answer
    1 l = 0.22 gal
    120 l = 26.4 gal
  4. How many ft are there in 90 mm?
    Show answer
    1 mm = 0.00328 ft
    90 mm = 0.295 ft
3. Calculate the following, giving your answers to 3 significant figures. Remember to add the units.
  1. How many square millimetres (mm2) are there in a square of side 70 mm?
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    area = 70 mm × 70 mm
    4900 mm2
  2. What is the mass (g) of 2 centilitres of water?
    Show answer
    1 centilitre of water has a mass of 10 g
    20.0 g
  3. What is the mass (kg) of 8 litres of water?
    Show answer
    1 litre of water has a mass of 1 kg
    8.00 kg
  4. How many litres (l) are there in 6 cubic metres (m3)?
    Show answer
    1 m3 = 1000 l
    6000 l
4. Calculate the following speed conversions, giving your answers to 3 significant figures. Remember to add the units.
  1. How many m/s are there in 50 in/s?
    Show answer
    1 in/s = 0.0254 m/s
    50 in/s = 1.27 m/s
  2. How many m/s are there in 6000 km/hr?
    Show answer
    1 km/hr = 0.2778 m/s
    6000 km/hr = 1670 m/s
  3. How many m/s are there in 90 mph?
    Show answer
    1 mph = 0.447 m/s
    90 mph = 40.2 m/s
  4. How many m/s are there in 7000 ft/s?
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    1 ft/s = 0.3048 m/s
    7000 ft/s = 2130 m/s
5. Write the following numbers to the specified number of significant figures.
  1. Write 0.01422 to 2 significant figures.
    Show answer
    0.014
  2. Write 198.943 to 5 significant figures.
    Show answer
    198.94
  3. Write 0.000112 to 2 significant figures.
    Show answer
    0.00011
  4. Write 885470 to 4 significant figures.
    Show answer
    885500
6. Give the following numbers in scientific notation. Write 1.23 × 104 as 1.23E4. Do not change the number of significant figures.
  1. Write 0.00138 in scientific notation.
    Show answer
    1.38E-3
  2. Write 669.54 in scientific notation.
    Show answer
    6.6954E2
  3. Write 0.01249 in scientific notation.
    Show answer
    1.249E-2
  4. Write 0.0000117 in scientific notation.
    Show answer
    1.17E-5
7. Give the following numbers in engineering notation (the exponent is a multiple of 3). Write 1.23 × 104 as 1.23E4. Do not change the number of significant figures.
  1. Write 130.985 in engineering notation.
    Show answer
    130.985E0
  2. Write 4084.1 in engineering notation.
    Show answer
    4.0841E3
  3. Write 0.00116 in engineering notation.
    Show answer
    1.16E-3
  4. Write 0.000192 in engineering notation.
    Show answer
    192E-6
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