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QuestionFill in the missing prefix or exponent in the following conversions: 1nN=10□N1 \mathrm{nN} = 10 \square \mathrm{N}, 1□N=106 N1 \square \mathrm{N} = 10^{6} \mathrm{~N}, 1□N=103 N1 \square \mathrm{N} = 10^{3} \mathrm{~N}, 1cN=10N1 \mathrm{c} \mathrm{N} = 10^{\mathrm{N}}.

Studdy Solution

STEP 1

Assumptions1. The table is dealing with metric prefixes. . The metric prefixes are used with the base unit Newton ().
3. The metric prefixes and their corresponding powers of ten are as follows - n (nano) = 10−910^{-9} - µ (micro) = 10−610^{-6} - m (milli) = 10−310^{-3} - c (centi) = 10−10^{-} - d (deci) = 10−110^{-1} - da (deka) = 10110^{1} - h (hecto) = 1010^{} - k (kilo) = 10310^{3} - M (mega) = 10610^{6} - G (giga) = 10910^{9}

STEP 2

For the first row, we know that 1n=10□1 \mathrm{n} =10^{\square} \mathrm{}. We know from our assumptions that n (nano) corresponds to 10−910^{-9}, so we can substitute this in to find the missing exponent.
1n=10−9=10□1 \mathrm{n} =10^{-9} \mathrm{} =10^{\square} \mathrm{}

STEP 3

olving for the missing exponent, we find that □=−9\square = -9.

STEP 4

For the second row, we know that 1□=1061 \square \mathrm{} =10^{6} \mathrm{}. We know from our assumptions that 10610^{6} corresponds to M (mega), so we can substitute this in to find the missing prefix.
1□=1MN1 \square \mathrm{} =1 \mathrm{MN}

STEP 5

olving for the missing prefix, we find that □=M\square = M.

STEP 6

For the third row, we know that 1□=1031 \square \mathrm{} =10^{3} \mathrm{}. We know from our assumptions that 10310^{3} corresponds to k (kilo), so we can substitute this in to find the missing prefix.
1□=1k1 \square \mathrm{} =1 \mathrm{k}

STEP 7

olving for the missing prefix, we find that □=k\square = k.

STEP 8

For the fourth row, we know that 1c=10□1 \mathrm{c} =10^{\square} \mathrm{}. We know from our assumptions that c (centi) corresponds to 10−210^{-2}, so we can substitute this in to find the missing exponent.
1c=10−2=10□1 \mathrm{c} =10^{-2} \mathrm{} =10^{\square} \mathrm{}

STEP 9

olving for the missing exponent, we find that □=−2\square = -2.
So, the completed table is\begin{tabular}{|l|l|} \hline n \mathrm{n} & =−9=^{-9} \mathrm{} \\ MN \mathrm{MN} & =6 =^{6} \mathrm{~} \\ k \mathrm{k} & =3 =^{3} \mathrm{~} \\ c \mathrm{c} & =−2=^{-2} \mathrm{} \\ \hline\end{tabular}

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