Question

Express the following using the prefixes of Table 1–4:

(a) \({\bf{1 \times 1}}{{\bf{0}}^{\bf{6}}}\;{\bf{volts}}\)

(b) \({\bf{2 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\;{\bf{meters}}\)

(c) \({\bf{6 \times 1}}{{\bf{0}}^{\bf{3}}}\;{\bf{days}}\)

(d) \({\bf{18 \times 1}}{{\bf{0}}^{\bf{2}}}\;{\bf{bucks}}\)

(e) \({\bf{7 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}\;{\bf{seconds}}\)

Short answer

The resultant expressions of the given values using prefixes for parts (a), (b), (c), (d), and (e) are \(1\;{\rm{megavolt}}\), \(2\;{\rm{micrometers}}\), \(6\;{\rm{kilodays}}\), \(18\;{\rm{hectobucks}}\), and \(0.7\;{\rm{microseconds}}\), respectively.

Step-by-step solution

Use of Prefixes

Prefixes

Prefixes are added at the beginning of words to modify their meaning. In the word unhappy, “un” is the prefix, and “re” is the prefix in the word rewrite.

To express the given value using a prefix, use Table 1–4.

\(\begin{aligned}{l}V = \left( {1 \times {{10}^6}\;{\rm{volts}} \times \frac{{1\;{\rm{megavolt}}}}{{{{10}^6}\;{\rm{volts}}}}} \right)\\ = 1\;{\rm{megavolt}}{\rm{.}}\end{aligned}\)

Metric (SI) prefixes

To express the given value using a prefix, use Table 1–4.

\(\begin{aligned}{l}d = \left( {2 \times {{10}^{ - 6}}\;{\rm{meters}} \times \frac{{1\;{\rm{micrometer}}}}{{{{10}^{ - 6}}\;{\rm{meters}}}}} \right)\\ = 2\;{\rm{micrometers}}{\rm{.}}\end{aligned}\)

SI prefixes

To express the given value using a prefix, use Table 1–4.

\(\begin{aligned}{l}t = \left( {6 \times {{10}^3}\;{\rm{days}} \times \frac{{1\;{\rm{kiloday}}}}{{{{10}^3}\;{\rm{days}}}}} \right)\\ = 6\;{\rm{kilodays}}{\rm{.}}\end{aligned}\)

Metric prefixes

To express the given value using a prefix, use Table 1–4.

\(\begin{aligned}{l}n = \left( {18 \times {{10}^2}\;{\rm{bucks}} \times \frac{{1\;{\rm{hectobuck}}}}{{{{10}^2}\;{\rm{bucks}}}}} \right)\\ = 18\;{\rm{hectobucks}}\end{aligned}\)

Applications of Prefixes

To express the given value using a prefix, use Table 1–4.

\(\begin{aligned}{l}t = 7 \times {10^{ - 7}}\;{\rm{seconds}}\\ = \left( {0.7 \times {{10}^{ - 6}}\;{\rm{seconds}} \times \frac{{1\;{\rm{microsecond}}}}{{{{10}^{ - 6}}\;{\rm{seconds}}}}} \right)\\ = 0.7\;{\rm{microseconds}}{\rm{.}}\end{aligned}\)