Questions: Knowing the value of an SI prefix as a power of 10 Complete each row of the table below by filling in the missing prefix or missing exponent. 1 mN = 10^-3 N 1 dN = 10^ N 1 cN = 10 N 1 N = 10^-9 N

Knowing the value of an SI prefix as a power of 10 Complete each row of the table below by filling in the missing prefix or missing exponent. 1 mN = 10^-3 N 1 dN = 10^ N 1 cN = 10 N 1 N = 10^-9 N
Transcript text: Knowing the value of an SI prefix as a power of 10 Complete each row of the table below by filling in the missing prefix or missing exponent. \begin{tabular}{|l} \hline 1 开 $\mathrm{N}=10^{-3} \mathrm{~N}$ \\ \hline $1 \mathrm{dN}=10^{\square} \mathrm{N}$ \\ \hline $1 \mathrm{c} \mathrm{N}=10 \square \mathrm{N}$ \\ $1 \square \mathrm{N}=10^{-9} \mathrm{~N}$ \\ \hline \end{tabular
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Solution

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Solution Steps

Step 1: Understanding the SI Prefixes

SI prefixes are used to denote powers of ten. Here are the relevant prefixes for this problem:

  • "d" stands for deci, which is \(10^{-1}\).
  • "c" stands for centi, which is \(10^{-2}\).
  • "k" stands for kilo, which is \(10^{3}\).
  • "m" stands for milli, which is \(10^{-3}\).
  • "μ" stands for micro, which is \(10^{-6}\).
  • "n" stands for nano, which is \(10^{-9}\).
Step 2: Solving for \(1 \, \text{dN} = 10^{\square} \, \text{N}\)

The prefix "d" stands for deci, which is \(10^{-1}\). Therefore, \(1 \, \text{dN} = 10^{-1} \, \text{N}\).

Step 3: Solving for \(1 \, \text{cN} = 10^{\square} \, \text{N}\)

The prefix "c" stands for centi, which is \(10^{-2}\). Therefore, \(1 \, \text{cN} = 10^{-2} \, \text{N}\).

Step 4: Solving for \(1 \, \square \text{N} = 10^{-9} \, \text{N}\)

The prefix that corresponds to \(10^{-9}\) is "n" for nano. Therefore, \(1 \, \text{nN} = 10^{-9} \, \text{N}\).

Final Answer

\[ \begin{align_} 1 \, \text{dN} &= 10^{-1} \, \text{N} \quad \boxed{-1} \\ 1 \, \text{cN} &= 10^{-2} \, \text{N} \quad \boxed{-2} \\ 1 \, \text{nN} &= 10^{-9} \, \text{N} \quad \boxed{\text{n}} \end{align_} \]

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