Represent each of the following quantities in thecorrect SI form using an appropriate prefix: (a) 0.000 431 kg,(b) 35.3(103) N, (c) 0.005 32 km.

Step-by-Step Solution

Step 1

We are given the values $0.000431\;{\rm{kg}}$, $35.3\left( {{{10}^3}} \right)\;{\rm{N}}$ and $0.00532\;{\rm{km}}$.

We are asked to represent each of the given values in the correct SI form.

Step 2

(a)

To convert the quantities into correct SI form we will use the following relation.

Since $1\;{\rm{kg}} = {10^3}\,{\rm{g}}$, then\[\begin{array}{c} 0.000431\;{\rm{kg}} = \left( {0.000431\;{\rm{kg}}} \right)\left( {\frac{{{{10}^3}\;{\rm{g}}}}{{1\;{\rm{kg}}}}} \right)\\ = 0.431\;{\rm{g}} \end{array}\]

Step 3

(b)

To convert the quantities into correct SI form we will use the following relation.

Since $1\;{\rm{kN}} = {10^3}\,{\rm{N}}$, then\[\begin{array}{c} 35.3\left( {{{10}^3}} \right)\;{\rm{N}} = \left( {35.3 \times {{10}^3}\;{\rm{N}}} \right)\left( {\frac{{1\;{\rm{kN}}}}{{{{10}^3}\;{\rm{N}}}}} \right)\\ = 35.3\;{\rm{kN}} \end{array}\]

Step 4

(c)

To convert the quantities into correct SI form we will use the following relation.

Since $1\;{\rm{km}} = {10^3}\,{\rm{m}}$, then\[\begin{array}{c} 0.00532\;{\rm{km}} = \left( {5.32 \times {{10}^{ – 3}}\;{\rm{km}}} \right)\left( {\frac{{{{10}^3}\;{\rm{m}}}}{{1\;{\rm{km}}}}} \right)\\ = 5.32\;{\rm{m}} \end{array}\]

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