Question

complete each row of the table below by filling in the missing prefix or missing exponent.
1 (square)g = (10^{-9}) g
1 (square)g = (10^{-1}) g
1 kg = (10^{square}) g
1 cg = (10^{square}) g

Explanation:

Step1: Recall nano - prefix

The prefix "nano -" (n) represents $10^{-9}$. So for $10^{-9}\ \text{g}$, the prefix is "nano" and the unit is ng.

Step2: Recall deci - prefix

The prefix "deci -" (d) represents $10^{-1}$. So for $10^{-1}\ \text{g}$, the prefix is "deci" and the unit is dg.

Step3: Recall kilo - prefix

The prefix "kilo -" (k) represents $10^{3}$. Since $1\ \text{kg}=1000\ \text{g}$ and $1000 = 10^{3}$, the exponent is 3.

Step4: Recall centi - prefix

The prefix "centi -" (c) represents $10^{-2}$. So for $1\ \text{cg}$, it is equal to $10^{-2}\ \text{g}$, and the exponent is - 2.

Answer:

1. $1\ \text{ng}=10^{-9}\ \text{g}$
2. $1\ \text{dg}=10^{-1}\ \text{g}$
3. $1\ \text{kg}=10^{3}\ \text{g}$
4. $1\ \text{cg}=10^{-2}\ \text{g}$