Style Guide for Homeworks

There are multiple ways to earn full credit on your assignments. Along with a correct value, answers are expected to include units and to be in a reasonable notation. Reasonable notation would be an answer that does not have infinite digits (e.g. cannot equal 12389243.9343 joules, but must be written as 12.4 megajoules or 1.2e6 joules)

Calculations

Explicitly show how you calculate your numbers. To make your calculations using python make sure your units are defined in a variable name (e.g. speed_in_km, time_hour, energy_density_joule_per_kg). The computer may output a long answer full of digits that don't need to be displayed. Make your answer into a reasonable notation by explaining it in a text (markdown) cell at the bottom of your work

Showing your work

Handwritten

You may turn in handwritten equations that show your mathematical reasoning and intention. Handwritten assignments with an image of the work done uploaded onto sagemathcloud. Handwriting must be legible and include units.

Advanced/Optional

Some of you may want to use advanced options for your work. You may use these tools, but we can't provide lots of help or support on these either in this class.

Optional: Code with the pint library

  • Using the pint library is completely optional when working on assignments.
  • This allows the units to be multiplied and divided with the resulting units being carried out into the answer.
  • This is helpful yet advanced tool, to learn more check out the pint tutorial

Optional style: LaTeX

  • If you decide to use markdown/LaTeX for your calculations, do not stress about the alignment. It doesn't have to look perfect, your work and understanding is more important than how it looks.
  • This form of showing work is advanced and completely optional.
  • You can learn more in [th
In [ ]:
# Question 1: Unit conversion

Please show the details of your work to answer these questions.

a) If you drive 20 miles, how many kilometers is that?

.62 miles = 1 kilometer
20/.62 = 32.26 kilometers


b) My car is traveling at 30 miles per hour, how many meters
per second is that?

1609.34 meters = 1 mile
1609.34*30 = 48,280 meters per hour
48,280/60 = 805 meters per minute
805/60 = 13 meters per second
In [4]:
1609.34*30
48280/60
805/60
Out[4]:
13.416666666666666
In [1]:
1 kilometer is .62 miles

20/.62
Out[1]:
32.25806451612903

Question 2: Scientific notation

Convert the following numbers to scientific notation.

Perform the following operations using scientific notation.

  1. Write out 3.5 trillion in scientific notation

35e11

  1. Write out 2.4 kJ in joules

.001 kilojoules = 1 joule 2.4/.001 = 2400 joules 24e2 joules

  1. How many GW is 14 TW?

1 GW = .001 TW 14/.001 = 14000 GW 14e3

In [11]:
14/.001
14e3
Out[11]:
14000.0
In [9]:
24e2
Out[9]:
2400.0
In [6]:
35e11
Out[6]:
3500000000000.0

Question 3: Exponential Growth

If the energy use in a country is increasing at 3 percent per year, by what fraction will it increase in 10 years?

.03 = 3/10

3^10 = 59e3 100^10 = 1e20

59e3/1e20

In [17]:
59e3/1e20
Out[17]:
5.9e-16
In [12]:
(3/100)*10
Out[12]:
0.3

Question 4: Linear Growth

The amount of gasoline that a car uses is linearly related to the distance it travels. Write an equation for this relationship for a 2015 Honda Civic. If this car is driven 1000 miles, how much gasoline will it use?

Distance = 1000 miles 2015 Honda Civic mpg in the city = 22 mpg 2015 Honda Civic mpg on the highway = 31 mpg

1000/22 = 45 gallons per 1000 miles in the city 1000/31 = 32 gallons per 1000 miles on the highway

In [13]:
1000/22
Out[13]:
45.45454545454545
In [14]:
1000/31
Out[14]:
32.25806451612903
In [ ]: