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. Express your answer in scientific notation to one significant figure or use a prefix on the unit.

Answer 1

To express the mass of the pill in grams, you can write it in scientific notation as 5.0 x 10^-3 g or in milligrams as 5 mg.

Step-by-step explanation:

To express the mass of the pain-relieving pill in grams, we can either use scientific notation or a metric prefix. The mass of the pill is given as 0.005 g. To express it in scientific notation, we write it as 5.0 x 10-3 g. This means the mass is 5.0 times 10 raised to the power of -3 grams. Alternatively, we can express the mass in milligrams. Since 1 gram is equal to 1000 milligrams, the mass of the pill can be written as 5 mg.

Answer 2

5 mg,
`5\cdot 10^(-3)g`

Step-by-step explanation:

First of all, let's rewrite the mass in grams using scientific notation.

we have:

m = 0.005 g

To rewrite it in scientific notation, we must count by how many digits we have to move the dot on the right - in this case three. So in scientific notation is

`m=5\cdot 10^(-3)g`

If we want to convert into milligrams, we must remind that

1 g = 1000 mg

So we can use the proportion

`1 g : 1000 mg = 0.005 g : x`

and we find

`x=((1000 mg)(0.005 g))/(1 g)=5 mg`