When numbers are very small or very large, it is convenient to either express the value in scientific notation and/or by using a prefix with the unit. a pain-relieving pill has a mass of 0.005 g. express the pill’s mass in grams using scientific notation or in milligrams.

The mass of the pill is m = 0.005 g.

Note that
     1/10 = 10⁻¹
  1/100 = 10⁻²
1/1000 = 10⁻³

1 milligram is written in standard notation as 1 mg.

The mass may be written as


Note also that
1 g = 1000 mg = 10³ mg

Therefore


Because 10⁻³ * 10³ = 10⁽⁻³⁺³⁾ = 10⁰ = 1, therefore m = 5.0 mg

 The mass of the pill is 5.0 x 10⁻³ g or 5.0 mg.

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