1.2 Units and standards  (Page 5/17)

Identify some advantages of metric units.

What are the SI base units of length, mass, and time?

What is the difference between a base unit and a derived unit? (b) What is the difference between a base quantity and a derived quantity? (c) What is the difference between a base quantity and a base unit?

For each of the following scenarios, refer to [link] and [link] to determine which metric prefix on the meter is most appropriate for each of the following scenarios. (a) You want to tabulate the mean distance from the Sun for each planet in the solar system. (b) You want to compare the sizes of some common viruses to design a mechanical filter capable of blocking the pathogenic ones. (c) You want to list the diameters of all the elements on the periodic table. (d) You want to list the distances to all the stars that have now received any radio broadcasts sent from Earth 10 years ago.

The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix. For example, 47 Ts would be rewritten as $4.7\times {10}^{13}\text{s.}$ (a) 980 Ps; (b) 980 fs; (c) 17 ns; (d) $577\mu \text{s}.$

The following times are given in seconds. Use metric prefixes to rewrite them so the numerical value is greater than one but less than 1000. For example, $7.9\times {10}^{\mathrm{-2}}\text{s}$ could be written as either 7.9 cs or 79 ms. (a) $9.57\times {10}^5\text{s;}$ (b) 0.045 s; (c) $5.5\times {10}^{\mathrm{-7}}\text{s;}$ (d) $3.16\times {10}^7\text{s.}$

The following lengths are given using metric prefixes on the base SI unit of length: the meter. Rewrite them in scientific notation without the prefix. For example, 4.2 Pm would be rewritten as $4.2\times {10}^{15}\text{m.}$ (a) 89 Tm; (b) 89 pm; (c) 711 mm; (d) $0.45\mu \text{m}\text{.}$

The following lengths are given in meters. Use metric prefixes to rewrite them so the numerical value is bigger than one but less than 1000. For example, $7.9\times {10}^{\mathrm{-2}}\text{m}$ could be written either as 7.9 cm or 79 mm. (a) $7.59\times {10}^7\text{m;}$ (b) 0.0074 m; (c) $8.8\times {10}^{\mathrm{-11}}\text{m;}$ (d) $1.63\times {10}^{13}\text{m.}$

The following masses are written using metric prefixes on the gram. Rewrite them in scientific notation in terms of the SI base unit of mass: the kilogram. For example, 40 Mg would be written as $4\times {10}^4\text{kg.}$ (a) 23 mg; (b) 320 Tg; (c) 42 ng; (d) 7 g; (e) 9 Pg.

The following masses are given in kilograms. Use metric prefixes on the gram to rewrite them so the numerical value is bigger than one but less than 1000. For example, $7\times {10}^{\mathrm{-4}}\text{kg}$ could be written as 70 cg or 700 mg. (a) $3.8\times {10}^{\mathrm{-5}}\text{kg;}$ (b) $2.3\times {10}^{17}\text{kg;}$ (c) $2.4\times {10}^{\mathrm{-11}}\text{kg;}$ (d) $8\times {10}^{15}\text{kg;}$ (e) $4.2\times {10}^{\mathrm{-3}}\text{kg.}$