Examples - Conversion between Levels of Powers of Ten

Example 1.14:
Convert 20 kHz to megahertz.
Note:
kilohertz (kHZ) is a unit of measurement for the frequency of an ac waveform.

Solution:
Replace the prefix by its corresponding power of ten.
The conversion factor is

                                      1 MHz = 10^6 Hz
In the power-of-ten format:
20 kHz
= (20 x 10^3 Hz) x (1 MHz / 10^6 Hz)
= 20 x 10^3 x 10^-6 MHz
= 20 x 10^-3 MHz
= 0.02 MHz

Example 1.15:
Convert 0.01 ms to microseconds.

Solution:
The conversion factor is

                                          1 ms = 10^-6 s

In the power-of-ten format:
0.01 ms = 0.01 x 10^-3 s
= (0.01 x 10^-3 s) x (1 ms / 10^-6 s)
= 0.01 x 10^-3 x 10^6 ms
= 0.01 x 10^3 ms
= 10 ms

Example 1.16:
Convert 0.002 km to millimeters.


Solution:
The conversion factor is

                                            1 mm = 10^-3 m

In the power-of-ten format:
0.002 km = 0.002 x 10^3 m
= (0.002 x 10^3 m) x (1 mm / 10^-3 m)
= 0.002 x 10^3 x 10^3 mm
= 0.002 x 10^6 mm
= 2000 mm