Monday, June 27, 2011

Practice with logarithmic scales - Richter and decibel.

a) There was a 7.6 earthquake in Mindanao in the Philippines and a 5.7 aftershock three days later. Rounded to the nearest multiple of 10, how much stronger was the bigger quake?

b) An earthquake registering 5.7 is recorded one morning, and in the afternoon, another quake 27 times stronger is felt. Give the Richter reading of the second stronger quake. (Nearest tenth.)

c) What is the decibel reading of a sound that has 7 times more energy than a 75 decibel reading. (Nearest decibel.)

d) One singer is measured at 64 dB. Eight singers at the same level would have eight times more energy. To the nearest decibel, what is the decibel level of the eight singer chorus?

e)  How much more energy is there in a reading of 75 dB compared to 64 dB.  Round to the nearest whole number.

Answers in the comments.

Friday, June 24, 2011

Practice for underflow and overflow in scientific notation.

Here is a link to a previous post about scientific notation, underflow and overflow.

Consider 80^80.  If you enter this into your calculator, you will likely get an overflow error because the answer is more than 10^100.  Here is how we can get around this, by splitting the number into two parts that are less than 10^100 and multiplying them together.

80^40 = 1.329227996 x 10^76

If we multiply 80^40 by 80^40, we will get 80^80.  We need to square 1.329227996 to get the new significand, and the new exponent will be 10^(76+76) = 10^152

1.32922² = 1.766825808..., but since we only squared the number with six significant digits, we can only trust the answer to five significant digits, so our best answer is 1.7668 x 10^152.

More practice.

a) 40^80


Answers in the comments.

Wednesday, June 22, 2011

Changing repeating decimals into fractions in lowest terms.

Using Blogger editing, it's a little tricky to put a bar over a group of numbers, but there is a strikethrough option, so I'm going to use that. To write .16161616...., I'll type .16 and to type .1666666..., I'll type .16.

Sorry if it's a little hard to read.

Method for changing from repeating decimal to fraction in lowest terms.

1. Call the repeating decimal x.
2. Multiply x by a power of ten that has as many zeros as there are digits in the repeating part.
3. Subtract x from the bigger number, which will cancel out the repeating part.
4*. IF the subtraction gives you a decimal number, multiply by some power of ten so you get (whole number times) x = (some other whole number)
5. Divide both sides of the equation by the number multiplying x.
6. Reduce the fraction to lowest terms.

Example #1: .16 = 0.1616161616....
1. x = 0.16161616...
2. Because the repeating part has two digits, multiply x by 100 to get 100x = 16.16161616....
3. 100x - x = 16.1616161616... - 0.1616161616...
which reduces to 99x = 16.
step 4 isn't needed.
5. x = 16/99, which is reduced to lowest terms.

Example #2: .16 = 0.166666....
1. x = 0.16666...
2. Because the repeating part has one digit, multiply x by 10 to get 10x = 1.6666....
3. 10x - x = 1.66666... - 0.166666...
which reduces to 9x = 1.5
4. 1.5 isn't a whole number, so multiply by 10 on both sides to get 90x = 15.
5. x = 15/90, which is not in lowest terms.
6. 15/90 = 5/30 = 1/6.

Practice problems.

a) Find the fraction for .23
b) Find the fraction for .23
c) Find the fraction for .234

Answers in the comments.

Tuesday, June 21, 2011

Practice problems for homework 1 of Summer 2011.

Change these numbers in Hindu-Arabic to Roman numerals.

648 = ______

15,781 = _____

Change these numbers in Roman numerals to Hindu-Arabic.

DCXCIV = ____

Find the approximation of 7/37 to the following number of decimal places and find the exact repeating decimal representation.

7/37 to the nearest tenth = _____
7/37 to the nearest hundredth = _____
7/37 to the nearest thousandth = ____

Repeating decimal representation = _____

Find the prime factorization of 48.

Find all the factors of 48.

Answers in the comments.

Monday, June 20, 2011

Link to notes about four great mathematicians.

Here is a link to a post about Archimedes, Newton, Euler and Gauss.

Syllabus for Summer 2011

Math 15: Math for Liberal Arts
Summer 2011
Instructor: Matthew Hubbard
Text: no required text. If you want a text, personal recommendations can be made
Class website:
Office hours: Math lab G-201 T-Th 9:20-9:50 am (also available by appointment)
Scientific calculator required (TI-30IIXs, TI-83 or TI-84 recommended)
Class hours MTWTh: 10:00 am - 12:15 pm, G-207

Important academic schedule dates:
Last date to add, if class is not full: Sat., June 25
Last date to drop class, no W on transcript: Thurs., June 30
Last date to withdraw from class, W on transcript: Thurs., July 20

Monday, July 4: Independence Day

Midterm and Finals schedule:
Half Midterm 1: Thursday, June 30
Full Midterm: Thursday, July 7
Half Midterm 2: Thursday, July 21
Comprehensive Final Thursday, July 28

Quiz schedule (most Tuesdays and Thursdays) no make-up quizzes given
6/21 6/23 6/28 7/5 7/12
7/14 7/19 7/26

Grading Policy
Homework to be turned in: Assigned every Tuesday and Thursday, due the next class
(late homework accepted at the beginning of next class period, 10% off grade)
If arranged at least a week in advance, make-up midterms (and half midterms) can be given.

The lowest two scores from homework and the lowest two scores from quizzes will be removed from consideration before grading.

Grading system
Quizzes 25%* best 2 out of three of these grades
Midterm 1 25%* best 2 out of three of these grades
Midterm 2 25%* best 2 out of three of these grades
Labs 5% in-class group and individual work
Homework 20%
Final 25%

Anyone who misses less than two homework assignments and gets a higher percentage score on the final than the weighted average of all grades combined will get the final percentage instead deciding the final grade.

Academic honesty: Your homework, exams and quizzes must be your own work. Anyone caught cheating on these assignments will be punished, where the punishment can be as severe as failing the class or being put on college wide academic probation. Working together on homework assignments is allowed, but the work you turn in must be your own, and you are responsible for checking its accuracy.

Class rules: Cell phones and beepers turned off, no headphones or text messaging during class
You will need your own calculator and handout sheets for tests and quizzes. Do not expect to be able to borrow these from someone else.

Student Learning Outcomes

• Analyze an argument for validity using simple rules of logic, and if invalid identify the type of mistake made.
• Compute, with sophisticated formulas, such quantities as interest payments for amortized loans.
• Interpret patterns and draw inferences from them.

Students with disabilities

The Disabled Students Program Services (DSPS) should have your academic accommodation with the instructor. After the first day, I will accept these accommodations electronically or by hard copy on paper. If you need academic accommodation and have not yet applied, please call 510-464-3428 for an appointment.

Exam policies
Tests will be closed book and closed notes. Some information you will be expected to remember, other formulas and information will be provided. No sharing of calculators is allowed. You are responsible for knowing how to use your calculator to find answers.

The reciprocal relationship

The teacher will be on time and prepared to teach the class.
The students will be on time and prepared to learn.

The teacher will present the material to the best of his ability.
The students will absorb the material to the best of their ability. They will ask questions when topics are not clear.

The teacher will do his best to answer the questions the students ask about the material, either by repeating an answer with more details included or by taking a different approach to the material that might be clearer to some students.
The students will understand if the teacher feels a topic has been covered enough for the majority of the class and will accept questions being answered outside the class, either in extra time or through written communication.

The teacher will do his best to keep the class about the material. Personal details and distractions that are not germane to the class should not be part of the class.
The students will do their best to keep the class about the material. Questions that are not about the topic should be avoided. Distractions like cell phones and texting are not welcome when the class is in session.

The teacher will give assignments that will help the students master the skills required to pass the course.
The students will put in their best efforts to complete the assignments.
When the assignments are completed, the teacher will make every effort to get the assignments graded and back to the students in a timely manner, by the next class session whenever possible.

The teacher will present real life situations where the skills being learned will be used when they exist. In math, sometimes a particular skill is needed in general to solve later problems that will have real life applications. Other skills have the application of “learning how to learn”, of committing an idea to memory so that committing other ideas to memory becomes easier in the long run.
The student has the right to ask “When will I use this?” when dealing with mathematical topics. Sometimes, the answer is “We need this skill for the next skill we will learn.” Other times, the answer is “We are learning how to learn.” Both of these answers are as valid in their way as “We will need this to understand perspective” or “We use this to balance our checkbooks” or “Ratios can be used to figure out costs” or other real life applications.