Solutions to Metric Unit Conversion Problems

Solution to Problem #1: The absolute exponential distance between kilo- (10³) and pico- (10¯¹²) is 10¹⁵. This problem can be done two ways.

Method #1: Convert km to pm

40,075.02 km times (10¹⁵ pm / 1 km) = 4.007502 x 10¹⁹ pm

4.007502 x 10¹⁹ pm / (140 pm per atom) = 2.86 x 10¹⁷ atoms

Method #2: Convert pm to km

140 pm times (1 km / 10¹⁵ pm) = 1.40 x 10¯¹³ km

40,075.02 km / (1.40 x 10¯¹³ km/atom) = 2.86 x 10¹⁷ atoms

Comment: this amount of Pd is:

2.86 x 10¹⁷ / 6.022 x 10²³ mol¯¹ = 4.75 x 10¯⁷ mol

and weighs:

4.75 x 10¯⁷ mol x 106.42 g mol¯¹ = 5.06 x 10¯⁵ g