Multiply 2.079x102 by 0.082x10-1, taking into account significant figures.

Question

anonymous · Answer

$$2.079\times10^2$$has four significant digits (2.079) and $$0.082\times 10^{-1} =8.2\times10^{-3}$$has two significant digits. Now these significant digits tell us how accurate the final result can be, and hence are limited by the lowest number of significant digits in the calculation. So the final answer has to be left with the lower number of significant digits as in the calculation http://en.wikipedia.org/wiki/Significant_figures > $$(2.079\times10^2)\times(8.2\times10^{-3}) =17.0478\times10^{-1}=1.70478$$ according to the rule about the lowest number of significant digits (for multiplication and division), we shave off the digits after the first 7 in the answer to obtain $$1.7$$ as the final answer.