Question

Fish can swim in depths as deep as 9.5 km. How many meters is this? How many mm?

Answer 1

`9.5xx10^3 m`
`9.5xx10^6 mm`

Explanation:

In order to compute the number of meters in 9.5 kilometers, we're going to use dimensional analysis (method that allows you to convert from one unit of measurement to another by cancelling out unwanted units) and the relationship below:

For questions like this I use the following technique:

`"Quantity Given" xx "Conversion Factor" = "Quantity Sought"`

`color(indigo)("Quantity Given:"` 9.5 kilometers

`color(coral)("Conversion Factor:"` 1000

`color(orange)("Quantity Sought:"` meters

Let's plug in our values:

`9.5cancel"km"xx(1000m)/(1cancel"km")` = `9.5xx10^3 m`

To go from kilometers to millimeters, we'll use the following relationship:

`color(brown)("Quantity Given:"` 9.5 kilometers

`color(red)("Conversion Factor:"` 1,000,000

`color(gray)("Quantity Sought:"` millimeters

`9.5cancel"km"xx(1,000,000mm)/(1cancel"km")` = `9.5xx10^6 mm`