Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

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Anis Elliott
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1 1, etc.. π, 2, 3, etc..

2 SECTION 1.1 A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money, but not cents!) However, they do not include fractions or decimals. The digits in a whole number have place value. Place Value Three- Digit Groups (separated by commas) Billions group Thousands group Millions group Ones group Verbal Form: Trillions group 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) Standard Notation: Uses only digits (0 through 9) and commas to state the number. 16 million = 16,000,000 Expanded Form: States the standard form of each place value. 31,567 3 is the place value for ten thousands so this represents 30,000 1 is the place value for thousands, so this represents 1,000 5 is the place value for hundreds, so this represents is the place value for tens, so this represents 60 7 is the place value for ones, so this represents 7 ones or 7 31, 567 in Exanded Form is 30, ,

3 Rounding Whole Numbers: Step 1: Locate the rounding digit, which is the digit at the place value you are rounding to. Step 2: Look at the digit directly to the right of the rounding digit. This is the test digit. If the test digit is < 5 (less than 5), keep the rounding digit the same and change all digits to the right of it to 0. If the test digit is 5 (greater than or equal to 5), then increase the rounding digit by 1 and change all the digits to the right of it to 0. On a number line, numbers are written so that ascending numbers are to the right. 10 is to the left of 20 on the number line, so 20 is greater than 10 (20 > 10). It can also be stated that descending numbers are to the left, so 10 is less than 20 (10 < 20) Ask "is 48 closer to 40 or 50?" It is closer to 50, it is about 50. Ask "is 81 is closer to 80 or 90?" It is closer to 80. It is about 80. Round off the same way for larger numbers Is 1888 closer to 1000 or 2000? 1888 is closer to Is 43,556 closer to 40,000, or 50,000? Compare the first two numbers. 43 is closer to 40 than 50. It is 40,000. "Tricky" numbers are those with 5 as the number that decides. Is 650 closer to 600 or 700? On a number line 650 is half way. Math has a rule for this. When the digit is 5 or greater, round up. When the digit is less than 5, round down. Example: Round 24 to the nearest ten. Round 36 to the nearest ten Rounds down Rounds up You may need to estimate to a certain place. Look at the number in the place to the right. Then round. Round 684 to the tens place. The number 4 in the ones place to the right of the tens. It rounds down to 680. Round 6423: to the nearest ten is to the nearest hundred is to the nearest thousand, it is Round 589,457: to the nearest ten, it is. to the nearest hundred, it is. to the nearest thousand, it is. to the nearest ten thousand is. to the nearest hundred thousand is. You can round it to the nearest million, it is 1,000,

4 Adding and Subtracting Whole Numbers Addition Terms: The numbers being added are called addends. Subtraction Terms: The number you are taking away is the subtrahend, the number you are subtracting from is the minuend, and the answer is the difference. Mathematical properties are often used to simplify computation. Below are three addition properties stated in words, shown with a numeric example, and shown with an algebraic example. The Zero Property of Addition is also called the Identity Property of Addition. Associative Property of Addition When numbers or variables are added, for example (2 + 3) + 4 = 2 + (3 + 4) and (a + b) + c = a + (b + c) The addends can be grouped in different ways without changing the result. Commutative Property of Addition When numbers or variables are added, for example = and a + b = b + a, The order of the addends can be changed without changing the result. Zero Property of Addition When 0 is added to a number or variable, for example, = 2 and a + 0 = a, the result is the same number or variable. These properties can be used when adding numbers in your head. Example: = ( ) + (10 + 8) = ( ) + (7+ 8) = = 355 Estimating Sums and Differences When an exact answer is not necessary, an estimate can be used. The most common method of estimating sums and differences is called front-end rounding, which is to round each number to its largest place value, so that all but the first digit of the number is 0. Examples: Estimate 4, Round 4,894 to the nearest thousand. 4,894 5,000 Round 429 to the nearest hundred Add the rounded numbers. 5, = 5,400 The actual answer is 4, = 5353, which is close to 5,400. If both addends are rounded up, the estimated sum will be greater than the actual sum, and if both addends are rounded down, the estimated sum will be less than the actual sum. Such generalizations are not possible with subtraction. Estimate 6, What is the largest place value of 6,209? Round to the nearest. 6,209 -> What is the largest place value of 383? Round to the nearest > Subtract the rounded numbers. - = The actual answer is 6, = 5826 How close was your estimate?

Pictograph A pictograph uses an icon to represent a quantity of data values in order to decrease the size of the graph. A key must be used to explain the icon.

Very simplistic Bar graph A bar graph displays discrete data in separate columns. A double bar graph can be used to compare two data sets.

5 Pictograph A pictograph uses an icon to represent a quantity of data values in order to decrease the size of the graph. A key must be used to explain the icon. Advantages Easy to read Visually appealing Handles large data sets easily using keyed icons Disadvantages Hard to quantify partial icons Icons must be of consistent size Best for only 2-6 categories Very simplistic Bar graph A bar graph displays discrete data in separate columns. A double bar graph can be used to compare two data sets. Categories are considered unordered and can be rearranged alphabetically, by size, etc. Advantages Visually strong Can easily compare two or three data sets DisadvantagesGraph categories can be reordered to emphasize certain effects Use only with discrete data Line graph A line graph plots continuous data as points and then joins them with a line. Multiple data sets can be graphed together, but a key must be used. Advantages Can compare multiple continuous data sets easily Interim data can be inferred from graph line Disadvantages Use only with continuous data 1999 Quarterly Financial Data for NIKE 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Year st Qtr 2nd Qtr 3rd Qtr 4th Qtr

Example of Real World graphs The following graph has two sets of data overlaying each other. One is a scattered diagram with connected dots. The other is a bar graph.

6 Example of Real World graphs The following graph has two sets of data overlaying each other. One is a scattered diagram with connected dots. The other is a bar graph. They both share the same x-values, which in this case are levels of education. The y-values for the bar graph (Median Weekly Earnings) are on the left, since earnings is represented by dollars. The y-values for the scattered diagram (Unemployment Rates) are on the right, since unemployment rates are represented as percentages. A sample data point would as follows: People with an Associate Degree have a median weekly earnings of about $700 and about a 3% unemployment rate.

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) WHOLE NUMBERS REVIEW A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money,