Hello, Kay,
The metric base unit for mass is the gram. We can set up the following relationships (check a metric conversion table). We make these relationships into conversion factors using grams:
:
(e.g., 1cg = 1.00E-02g)
Expressed as conversion factors:
g/cg = 1.00E-02
g/Mg = 1.00E+6, or by inverting, we have:
Mg/g = 1.00E-06
Start with the amount given and multiply by the conversion factors such that the units cancel until the value is expressed as Mg (I needed to invert the g/Mg unit so that g would be on the bottom and cancel out ):
2.90E-07cg * 1.00E-02 g/cg *1.00E-06 Mg/g
Cancel the units (cg/cg and g/g) and we see that the only unit left is Mg. That means we've likely set up the conversion factors correctly, so simply multiply the three values to give the final result:
2.90E-15 Mg
[Note that you don't really need a calculator. The three exponents of 10 are -7, -2, and -6. Since they are being multiplied, just add them to get -15, the resulting exponent. Since two of the three numbers are simply "1," the calculation is easy: 2.90 * 1 * 1 = 2.90. So the answer is 2.90E-15 Mg.
This problem illustrates a key advantage of the metric system - the ease of converting between magnitude units (they are all a factor of 10). E.g., 1,000 meters = 1 kilometer. But in English units we have 5,280 feet/mile, or 12 inches/foot. Tougher to do without a calculator.
