David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: Number Discoveries and Developments, Exercise 24: Practice 3

With the development of the metric system, it became easier to compare, multiply and divide quantities because of the use of prefixes.

How many picograms are in a kilogram?

With the development of the metric system, it became easier to compare, multiply and divide quantities because of the use of prefixes.

How many nano bytes are in a gigabyte?

With the development of the metric system, it became easier to compare, multiply and divide quantities because of the use of prefixes.

How many femtometers are in a millimeter?

With the development of the metric system, it became easier to compare, multiply and divide quantities because of the use of prefixes.

What fraction of a megameter is an attometer?

With the development of the metric system, it became easier to compare, multiply and divide quantities because of the use of prefixes.

What fraction of a decigram is a microgram?

Evaluate the following. Write your answer as integer or fraction.

$(3^{-3}÷9^{-2})÷6^2$

In physics, dimensional analysis is often used to verify that the units in a formula produce the correct units for the answer. This process was first published by François Daviet de  Foncenex in $1761$, and was later developed by other scientists, for example James Clerk Maxwell.
In $1784$, Charles-Augustin de Coulomb discovered that the force of attraction between two electric charges, $q_1$ and $q_2$ can be calculated using the formula $F=\frac{k{q}_1{q}_2}{r^2}$, where: each electric charge is measured in coulombs ($C$), $r$ (the distance between the charges) is measured in meters, the constant $k$ has the units ${\mathrm{Nm}}^2 {\mathrm{C}}^{-2}$.

Substitute these units into the formula and show that the formula produces the correct units of force, newtons ($\mathrm{N}$).

In physics, dimensional analysis is often used to verify that the units in a formula produce the correct units for the answer. This process was first published by François Daviet de  Foncenex in $1761$, and was later developed by other scientists, for example James Clerk Maxwell.

The electric potential ($V$) created by a charge $Q$ (measured in coulomb) at a distance $r$ (in meters) from the charge was discovered to be given by the formula $V=\frac{1}{4\pi {\epsilon }_0}\times \frac{Q}{r}$, where ${\epsilon }_0$ is measured in ${\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$. What should the units of electric potential be?