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= (1000)/(1000) * (0.005 \, g )/(1) = (1000 * 0.005 \, g)/(1000) = 5.0 \, g * 10^(-3)`

Note also that
1 g = 1000 mg = 10³ mg

Therefore

`m=(5.0 * 10^(-3) \, g)*(10^(3) \, (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.