Question

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.

Answer 1

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
$m= \frac{1000}{1000} \times \frac{0.005 \, g }{1} = \frac{1000 \times 0.005 \, g}{1000} = 5.0 \, g \times 10^{-3}$

Note also that
1 g = 1000 mg = 10³ mg

Therefore
$m=(5.0 \times 10^{-3} \, g)*(10^{3} \, \frac{mg}{g})$

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

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