Final answer:
Thomas Savery's "Miner's Friend" is the least efficient, followed by Thomas Newcomen's Atmospheric Engine, and James Watt's Steam Engine is the most efficient.
Step-by-step explanation:
To rank the steam engines from least efficient to most efficient, we must consider the advancements and design improvements made over time. The earliest of the three was Thomas Savery's "Miner's Friend", which was the first commercial steam engine used to pump water out of mines. However, this design was quite primitive and not very efficient. The next development came with Thomas Newcomen's Atmospheric Engine, which was an improvement but still required a lot of fuel and had limited pumping height. Despite these drawbacks, its mechanical simplicity saw it widely adopted. The most efficient of the three was James Watt's Steam Engine. Watt made significant improvements to the steam engine, making it more efficient by requiring only a quarter as much fuel as Newcomen's and introducing an engine that provided rotating motion to power factory machinery.
The ranking, therefore, from least to most efficient is: Thomas Savery's "Miner's Friend", Thomas Newcomen's Atmospheric Engine, and James Watt's Steam Engine.