Chapter+Five

**Section 5.1** **5.2** **5.3**  **5.4**  **5.5**  **5.6**  **5.7**   **5.8**  **5.9**  **5.10**
 * Chapter 5 **
 *  Place value after the decimal point
 * Add ths to the place values on the left side of the decimal, so “tens” becomes “tenths”.
 * There is no “oneths” place. The first place to the right of the decimal is the tenths place
 * 
 * Reading decimal numbers (like saying them out loud)
 *  Decimal point = “and”
 * Say it like you would on left side of the decimal point (chapter one), say and, then say the numbers on the right just like you would on the left, but add ths to the last place value.
 * Really we don’t often say it that way. Usually we just say “six point three five seven four”
 * Rounding decimals and front-end rounding: This is done exactly the same way as rounding integers except that instead of changing all of the remaining digits to zeroes, they are just dropped because zeroes at the end of a decimal number do not matter. (Zeroes inside of other digits do, so they can’t be dropped, but zeroes on the right side of the number can be.)
 *  Round to the nearest cent or dollar: A dollar is the ones place 3.00 and the cents are the hundredths place 4.56 is 56 cents.
 * Adding decimals
 * The decimal points must line up!
 * Using zeros as placeholders, either in the top number or the bottom number so that both the top and bottom numbers have the same number of digits, at least to the right of the decimal.
 * Add just like you would with integers, and drop the decimal point straight down in the answer.
 * Subtracting decimals
 * Line up the decimal points
 * Definitely use zeros as placeholders!
 *  Remember to subtract the digit on the bottom from the one on the top (borrow if necessary)
 * The decimal also drops straight down into the answer.
 * Multiplying decimals
 * Don’t line up the decimals! Line up the numbers on the right side, regardless of where the decimal is. (The places values might not match up, but that is okay.)
 *  Multiply the same way you would with integers, ignoring the decimal point for now.
 * After adding up the results (like normal), count the number of digits to the right of the decimal point in both the top and the bottom numbers. Move the decimal point in the answer that many digits //from the right//.
 * Dividing decimals
 * The number on the outside of the division sign must be an integer, so you might have to move the decimal point over to the right.
 * However far you move it to the right, you have to move the decimal point in the number inside the divide sign that same distance to the right. If you run out of digits to the right, add enough zeroes to move it.
 * The number inside of the division sign does not have to be an integer.
 * Put the decimal point directly up in the answer from where it was after adjusting for the integer.
 *  It is okay to add zeroes after the decimal point, or to the right of the last digit after the decimal point if you need to be more precise in your answer. (Like carrying it out to the nearest thousandth.)
 *  Do the long division as normal, but there won’t be a remainder. Instead keep going after the decimal point until you get to the desired place value. Usually if it doesn’t say anything, hundredths is enough.
 * Repeating bar sign
 * A small bar (minus sign) above a number or group of numbers means that that number is repeated forever.
 * 4.33333333. . . would be written as 4.3 with a bar above the 3
 * Sometimes this gets rounded up, such as 3.666667
 *  Converting fractions to decimals such as 1/8: Divide the numerator (top number) by the denominator (bottom number). (8 into 1)
 *  Comparing fractions and decimals on a numberline
 * We have already learned how to locate fractions on a numberline. Decimals also get graphed on a numberline by guessing how close they are to the nearest integer.
 * Another way to compare fractions and decimals is to convert both to the same format. It is easiest to convert both to decimals rather than both to fractions.
 *  Mean, also known as Arithmetic Mean
 * Add up the numbers, divide by how many numbers there were.
 * 5+6+7+10 = 28 divided by 4 = 7 The mean of these numbers would be 7
 * The mean is usually not an integer, usually it is a decimal number.
 * This is the most common form of average, so if they say average and don’t specify another kind, use this method
 * Weighted Mean
 * This is used when one term has a different value than another. For example, your grades. If you have an A in one class and a B in another, it matters how many credits each class was to figure out what your GPA is. If the class with an A is worth 5 credits and the B class was only worth 2, you take 5 times 4.0 (what an A is worth) plus 2 times 3.0 (the value of a B). So you end up adding 4+4+4+4+4+3+3 and dividing that by 7 (the weighted number not the first value) to get 3.714
 * Median means that if you had the numbers in numerical order, it would be the very middle number
 * If you have an odd number of terms, arrange them in order from smallest to largest and circle the middle number – that’s the median
 * If you have an even number of terms, arrange them in order still, but take the two middle numbers, add them together and divide by 2 to get the median. If you get a decimal number, that’s fine.
 * Mode means the number or the thing that occurs the most often.
 * If 5 people are blondes, 3 are redheads and 2 are bald, blonde is the mode.
 * Write out the numbers in numerical order. Find the one that occurs the most – that is the mode.
 * Bimodal means that there are exactly two numbers that are tied for the most often.
 * If there are no numbers that occur more than others, or if there are more than two tied for the most, we say that there is no mode.
 * Variability (essentially range in this class) refers to the distance (difference) between the lowest term and the highest term.
 * Find the highest and lowest terms. Subtract the lowest from the highest – this is the range.
 * Square root
 * Square roots are described as “What number, times itself, equals the number under the square root sign?” 3 times 3 is 9, so 3 is the square root of 9.
 * Finding a square root without a calculator usually means trial and error and a whole lot of multiplying, because most square roots are ugly decimal numbers.
 *  Perfect squares are numbers that have square roots that are whole numbers. So 49 is a perfect square because 7 times 7 is 49.
 * Perfect squares might also show up on the test as a fraction with perfect squares as both numerator and denominator. In this case, the desired answer is a fraction rather than a decimal. I don’t know why.
 *  Pythagorean Theorem
 * Given a right triangle (one side is 90 degrees), A2 + B2 = C2
 * The hypotenuse is the side opposite the 90 degree angle. It will always be the longest side.
 * C is always the hypotenuse, A and B can be either of the other sides, it doesn’t matter which.
 * Finding the hypotenuse: Plug in the values for A and B. Square A and B and add together. Take the square root of this number and that is the answer for C.
 * Finding one of the other sides: Plug in the values for B and C. Square both B and C. Subtract the value of B2 from both sides. Take the square root and that is the length of the missing side.
 * Finding isosceles triangle sides: Isosceles triangles mean that the other two sides are the same length. In this case you would combine A and B (both unknown) as the same variable and call it 2A. (A + A = 2A) . So, plug in and square the value of C. Divide by 2 on both sides. Then take the square root of both sides and you will have the answer.
 * Solving equations with decimals: This is exactly the same as solving for X from chapter 2, but takes a bit longer without a calculator.
 *  Radius / Diameter
 * The diameter is the distance across a circle, through the center point. So if you measure the “width” of the circle at its biggest point, that is the diameter.
 * Diameter always uses a lowercase //d// for a variable.
 * Radius is one half of the diameter, or the distance from the edge of the circle to the center point.
 * Radius always uses a lowercase //r// for a variable.
 * Circumference of a circle
 * The circumference is the distance around the circle.
 * Circumference is calculated as the 2πr, and is expressed in units like inches or feet.
 * Pi
 * Pi is represented by the Greek letter: π
 *  It is a decimal number that never repeats, but is usually shortened to 3.14
 *  If you use the Pi symbol on your calculator, you will get a slightly different answer than if you use 3.14
 * Pi is equal to the circumference of a circle, divided by its diameter
 * Area of a circle
 * πr2
 * The surface area of a circle, expressed in squared units.
 * Volume of a cylinder
 * How much (water or anything) could be put inside of a cylinder (like a pop can)
 * The formula is essentially the area of the circular part of the cylinder, times the height of the cylinder: πr2h
 * Surface area of a rectangular solid
 * Just figure out the area of each of the sides (usually rectangles) and add them together.
 * Surface area of a cylinder
 * Much like the surface area of a rectangular solid, you are trying to find the area of the outside of the cylinder. This is the area of the top and bottom of the cylinder, which are the area of a circle (twice). But the “label” part of the cylinder is the height times the circumference of the circle. (Pretend that you cut the cylinder and roll out the label part – it makes a rectangle.