We want to use the given table to calculate how many nanometers are in a millimeter.
Unit of Length
Length (meter)
Decimeter
10^(- 1)
Centimeter
10^(- 2)
Millimeter
10^(- 3)
Micrometer
10^(- 6)
Nanometer
10^(- 9)
All the given units of length are expressed in terms of meters. Next, we will calculate the ratio of millimeters to nanometers. It divides a millimeter into parts with the length of one nanometer. The result is the number of nanometers in a millimeter.
1millimeter/1nanometer = 10^(- 3) meters/10^(- 9) meters
Now we have a quotient of two powers with the same base. Let's use the Quotient of Powers Property to evaluate the quotient.
Quotient of Powers Property
To divide powers with the same base, we can subtract their exponents.
Let's apply this property to our quotient! Notice that we have negative exponents but the Quotient of Powers Property works also for negative exponents. Also, we can forget about units for a moment for simplicity.
