A kilogram is 100,000 times greater than a centigram
Step-by-step explanation:
The table representing the relationship between grams and its sub-units is the following:
Microgram ([tex]\mu g[/tex]) = [tex]10^{-6}[/tex] grams (g)
Milligram (mg) = [tex]10^{-3}[/tex] grams (g)
Centigram (cg) = [tex]10^{-2}[/tex] grams (g)
Gram (g) = [tex]10^0[/tex] grams (g)
Kilogram (kg) = [tex]10^3[/tex] grams (g)
Let's now analyze the different statements given:
A microgram is 1,000 times greater than a milligram. --> FALSE. In fact, a microgram is [tex]\frac{10^{-6}}{10^{-3}}=0.001[/tex] times a milligram, so it is 1000 times smaller than a milligram.
A milligram is 10 times greater than a centigram. --> FALSE. In fact, a milligram is [tex]\frac{10^{-3}}{10^{-2}}=0.1[/tex] times a centigram, so it is 10 times smaller than a centigram.
A centigram is 100 times greater than a microgram. --> FALSE. In fact, a centigram is [tex]\frac{10^{-2}}{10^{-6}}=10^4=10,000[/tex] times a microgram, so it is 10,000 greater than a microgram.
A kilogram is 100,000 times greater than a centigram. --> TRUE. In fact, a kilogram is [tex]\frac{10^3}{10^{-2}}=10^5 = 100,000[/tex] times a centigram.
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