## Tuesday, September 22, 2015

### For the Monday-Wednesday class: Notes for September 21 and 23Also the notes for September 29 for the Tuesday Thursday class

Scales based on other powers of 10 besides 100 (percent) and murder rates per 100,000.

Fractions, decimals and percents.

Changing repeating decimals to fractions in lowest terms.

Approximating and simplifying square roots.

Rounding decimals.

Let's consider 3/7. If you type 3/7 into the calculator, you'll get 0.428571429. If we wanted to write the fraction with a bar over the repeating part, the answer would be
______
.428571

Usually, fractions like this are written as decimals rounded to the nearest tenth, hundredth or thousandth.  Let's do all three versions here.

3/7 rounded to the nearest tenth.
Step 1: Erase everything after the first digit, which gives us .4
Step 2: Because the left most digit we erased is a 2, we leave the .4 alone.
3/7 ~= .4 rounded to the nearest tenth.

3/7 rounded to the nearest hundredth.
Step 1: Erase everything after the second digit, which gives us .42
Step 2: Because the left most digit we erased is an 8, we change .42 to .43, rounding up.
3/7 ~= .43 rounded to the nearest hundredth.

3/7 rounded to the nearest thousandth.
Step 1: Erase everything after the third digit, which gives us .428
Step 2: Because the left most digit we erased is a 5, we increase .428 to .429.
3/7 ~= .429 rounded to the nearest thousandth.

Rounding error.

If we multiply 7 × 3/7, we get 3 exactly.  If we multiply 7 by a rounded version of 3/7, we won't get exactly 3. If we rounded the approximation off, when we multiply we will be below the target. If we round the approximation up, we will be above the target.

7 × .4 = 2.8, so we are 0.2 below 3.

7 × .43 = 3.01, so we are 0.01 above 3.

7 × .429 = 3.003, so we are 0.003 above 3.

## Tuesday, September 15, 2015

### Posts on Roman numerals

Here are links to previous practice problems dealing with Roman numerals.

Here are a few more practice problems, with answers in the comments.

702 = ______

2,598,960 = _____

Change these numbers in Roman numerals to Hindu-Arabic.
__
IVXXIX = ____

DCVII = ____

## Friday, September 11, 2015

### Notes for September 10 (Tues.-Thurs. class) and September 14 (Mon.-Wed. class)

Notes on logarithms. While there are other logarithmic scales including pH, we will be focusing on the bel system (usually written in decibels, or tenth of bels, so that 7.1 bels is written as 71 decibels or 71 dB) and the Richter scale, always written to the nearest tenth, like 4.5 or 3.0.

## Tuesday, September 8, 2015

### Notes for September 8 (Tuesday-Thursday) and September 9 (Monday-Wednesday)

The Monday-Wednesday class meets only one day this week, so the notes are split up.

Notes on contingency tables and probabilities based on contingency tables.

Notes on scientific notation.