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Convert the following masses into kilograms: a) 58475 μg b) 406 dg c) 1900 cg d) 65 Mg e) 945 Dg

Mathematics

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Step-by-step solution

15 steps

Here are the conversions of the given masses into kilograms:

Part a· 2 steps

Convert 58 475 μg58\,475\, \mu\text{g} to kilograms.

  1. Convert micrograms to grams.

    58 475 μg×1 g1 000 000 μg=0.058475 g58\,475\, \mu\text{g} \times \frac{1\, \text{g}}{1\,000\,000\, \mu\text{g}} = 0.058475\, \text{g}
  2. Convert grams to kilograms.

    0.058475 g×1 kg1 000 g=0.000058475 kg0.058475\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 0.000058475\, \text{kg}

    The mass is 0.000058475 kg\boxed{\text{0.000058475 kg}}.

Part b· 2 steps

Convert 406 dg406\, \text{dg} to kilograms.

  1. Convert decigrams to grams.

    406 dg×1 g10 dg=40.6 g406\, \text{dg} \times \frac{1\, \text{g}}{10\, \text{dg}} = 40.6\, \text{g}
  2. Convert grams to kilograms.

    40.6 g×1 kg1 000 g=0.0406 kg40.6\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 0.0406\, \text{kg}

    The mass is 0.0406 kg\boxed{\text{0.0406 kg}}.

Part c· 2 steps

Convert 1 900 cg1\,900\, \text{cg} to kilograms.

  1. Convert centigrams to grams.

    1 900 cg×1 g100 cg=19 g1\,900\, \text{cg} \times \frac{1\, \text{g}}{100\, \text{cg}} = 19\, \text{g}
  2. Convert grams to kilograms.

    19 g×1 kg1 000 g=0.019 kg19\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 0.019\, \text{kg}

    The mass is 0.019 kg\boxed{\text{0.019 kg}}.

Part d· 1 step

Convert 65 Mg65\, \text{Mg} to kilograms.

  1. Convert megagrams to kilograms.

    (Note: 1 Mg=1 000 kg1\, \text{Mg} = 1\,000\, \text{kg})

    65 Mg×1 000 kg1 Mg=65 000 kg65\, \text{Mg} \times \frac{1\,000\, \text{kg}}{1\, \text{Mg}} = 65\,000\, \text{kg}

    The mass is 65000 kg\boxed{\text{65000 kg}}.

Part e· 2 steps

Convert 945 Dg945\, \text{Dg} to kilograms.

  1. Convert decagrams to grams.

    945 Dg×10 g1 Dg=9 450 g945\, \text{Dg} \times \frac{10\, \text{g}}{1\, \text{Dg}} = 9\,450\, \text{g}
  2. Convert grams to kilograms.

    9 450 g×1 kg1 000 g=9.45 kg9\,450\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 9.45\, \text{kg}

    The mass is 9.45 kg\boxed{\text{9.45 kg}}.

Part f· 2 steps

Convert 1 854 mg1\,854\, \text{mg} to kilograms.

  1. Convert milligrams to grams.

    1 854 mg×1 g1 000 mg=1.854 g1\,854\, \text{mg} \times \frac{1\, \text{g}}{1\,000\, \text{mg}} = 1.854\, \text{g}
  2. Convert grams to kilograms.

    1.854 g×1 kg1 000 g=0.001854 kg1.854\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 0.001854\, \text{kg}

    The mass is 0.001854 kg\boxed{\text{0.001854 kg}}.

Part g· 1 step

Convert 23 tonnes23\, \text{tonnes} to kilograms.

  1. Convert tonnes to kilograms.

    (Note: 1 tonne=1 000 kg1\, \text{tonne} = 1\,000\, \text{kg})

    23 tonnes×1 000 kg1 tonne=23 000 kg23\, \text{tonnes} \times \frac{1\,000\, \text{kg}}{1\, \text{tonne}} = 23\,000\, \text{kg}

    The mass is 23000 kg\boxed{\text{23000 kg}}.

Part h· 2 steps

Convert 125 Hg125\, \text{Hg} to kilograms.

  1. Convert hectograms to grams.

    125 Hg×100 g1 Hg=12 500 g125\, \text{Hg} \times \frac{100\, \text{g}}{1\, \text{Hg}} = 12\,500\, \text{g}
  2. Convert grams to kilograms.

    12 500 g×1 kg1 000 g=12.5 kg12\,500\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 12.5\, \text{kg}

    The mass is 12.5 kg\boxed{\text{12.5 kg}}.

Part h(i)· 1 step

Convert 40 500 g40\,500\, \text{g} to kilograms.

  1. Convert grams to kilograms.

    40 500 g×1 kg1 000 g=40.5 kg40\,500\, \text{g} \times \frac{1\, \text{kg}}{1\,000\, \text{g}} = 40.5\, \text{kg}

    The mass is 40.5 kg\boxed{\text{40.5 kg}}.

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