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The central issue in converting units in the SI system is to figure out how many small units equal one big unit. Here is how to do it:

Take a conversion from millimeters to kilometers. Look at the power of ten next to kilo- in the chart: 10³. Now look at the power of ten next to milli- in the chart: 10^-3. Divide the power of ten next to the larger unit by the power of ten next to the smaller unit:

 103
———— = 106 (when dividing numbers raised 
 10-3        to an exponent, subtract exponents)
                       1 x 106 mm
 1 x 106 mm = 1 km or  ————————
                         1 km

This result says that there are 10⁶ (1,000,000) millimeters in 1 kilometer. Try another one: how many nanometers (the smaller unit) are there in 1 centimeter (the larger unit)? Nano- is 10^-9 and centi- is 10^-2.

 10-2
———— = 107 or 10,000,000   So there are 1 x 107 (10,000,000) nm in 1 cm.
 10-9

Examples:

How many mL are there in one L?
base    100
       ————— = 103  which means 1 L = 1,000 mL
milli-  10-3
How many pg are in one μg?
μ-      10-6
       ————— = 106  which means 1 μg = 1,000,000 pg
pico-   10-12
Now convert 5,897,000 pg to μg:
                  1 μg
5,897,000 pg × —————————— = 5.897 μg
               1,000,000 pg

 

1. How many pico-units are in one nano-unit?
2. How many pico-units are in one milli-unit?
3. How many nanometers are in one meter?
4. How many milliliters are in one kiloliter?
5. How many centimeters are in one megameter?
6. How many decimeters are in one kilometer?
7. How many femtometers are in one nanometer?
8. How many kilobytes are in one gigabyte?

9. Convert 54 nL to pL
10. Convert 42,000,000 pL to mL
11. Convert 4,009,450,000 nm to m
12. Convert 12 kL to mL
13. Convert 14 Mm to cm
14. Convert 4 km to dm
15. Convert 12 nm to fm
16. Convert 42,000,000 kB to GB