the table below shows metric units of mass, with the relationship of each unit to 1 gram represented as a…

Explanation:

Step1: Recall the relationship between powers of 10

To compare the magnitudes of the metric - mass units, we use the rules of exponents. If we have two numbers (a = 10^{m}) and (b = 10^{n}), then (\frac{a}{b}=10^{m - n}).

Step2: Analyze option A

A micro - gram is (10^{-6}) and a milli - gram is (10^{-3}). Then (\frac{10^{-6}}{10^{-3}}=10^{-6-(-3)} = 10^{-3}=\frac{1}{1000}), so a micro - gram is (\frac{1}{1000}) of a milli - gram, not 1000 times greater.

Step3: Analyze option B

A milli - gram is (10^{-3}) and a centi - gram is (10^{-2}). Then (\frac{10^{-3}}{10^{-2}}=10^{-3-(-2)}=10^{-1}=\frac{1}{10}), so a milli - gram is (\frac{1}{10}) of a centi - gram, not 10 times greater.

Step4: Analyze option C

A centi - gram is (10^{-2}) and a micro - gram is (10^{-6}). Then (\frac{10^{-2}}{10^{-6}}=10^{-2-(-6)} = 10^{4}=10000), so a centi - gram is 10000 times greater than a micro - gram, not 100 times greater.

Step5: Analyze option D

A kilo - gram is (10^{3}) and a centi - gram is (10^{-2}). Then (\frac{10^{3}}{10^{-2}}=10^{3-(-2)}=10^{5}=100000), so a kilo - gram is 100000 times greater than a centi - gram.

Answer:

A kilogram is 100,000 times greater than a centigram.