Since this is the first chapter, there is nothing you need to input. Just run the Notebook, and examine the output.

First, let's start by clearing all the variables.

Clear["Global`*"]

First, we load in some extra packages to define the conversions and units.

Needs["Miscellaneous`Units`"]
Needs["Miscellaneous`PhysicalConstants`"]

Let's find out about the Convert command

?Convert

Here is a simple example.

Convert[ 60 Mile/Hour, Feet/Second]

Convert[ 60 Mile/Hour, Meter/Second]

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Problem 8E

Let's do the homework problem. First, we use the convert function to change 1 Yard^2 into Feet^2. (Note the ^2 means to square.)

Convert[ 1 Yard^2, Foot^2]

If I had to to this on my own with out the computer, I would write

1 (Yard)^2 (3 Foot/Yard)^2

The other parts of this problem are similar.

Note, that the prefixes must be separated by a space for Mathematica to function properly. (See Centi Meter and Kilo Meter below. )

((SPECIAL NOTE: Since Kilogram is the fundamental MKS unit, this is an exception to the exception. See problem 34.))

Convert[ 1 Inch^2, (Centi Meter)^2]

1 (Inch)^2 ( 2.54 Centi Meter/Inch)^2

Convert[ 1 Mile^2, (Kilo Meter)^2]

1 (Mile)^2 (1.60934 Kilo Meter/Mile)^2

Convert[ 1 Meter^3, (Centi Meter)^3]

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Problem 20E

Since we loaded in the PhysicalConstants package, the SpeedOfLight is defined.

SpeedOfLight

Convert[ SpeedOfLight, Feet/(Nano Second)]

Convert[ SpeedOfLight, Milli Meter /(Pico Second)]

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Problem 22E

Convert[ 1 Year, Second]

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Problem 26E

Convert[ 3.0 10^-2 Mile/Hour, Meter/Second]

Convert[ 1.2 Mile/Hour, Meter/Second]

Convert[ 23 Mile/Hour, Meter/Second]

Convert[ 70 Mile/Hour, Meter/Second]

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Problem 34E

Let us see what Mathematica knows about AMU.

?AMU

Since a molecule of Water is 1 Oxygen atom plus 2 Hydrogen atom, 
each molecule of water is 18 AMU, we find:

Convert[ 18 AMU, Kilogram]

Here we convert Kilogram to AMU, and then divide by 18.

Convert[ 1.4 10^21 Kilogram, AMU]/( 18 AMU/(Water Molecule))