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Place Value and Names for Numbers. 1.2. Place Value. The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 can be used to write numbers. The whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, … The position of each digit in a number determines its place value. Examples.

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  1. Place Value and Names for Numbers 1.2

  2. Place Value The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 can be used to write numbers. The whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, … The position of each digit in a number determines its place value.

  3. Examples Find the place value of the digit 4 in each whole number. a. 48,761 b. 249 c. 524,007,656 ten-thousands tens millions

  4. Whole Numbers in Words and Standard Form The whole number 1,083,664,500 is written in standard form. Each group of three digits is called a period.

  5. Examples Write each number in words. a. 36 b. 487 c. 32,984 thirty-six four hundred eighty-seven thirty-two thousand, nine hundred eighty-four

  6. Whole Numbers in Words and Standard Form

  7. Examples Write each number in standard form. a. seventy-two b. nine hundred six c. eight thousand, six hundred fifty-four 72 906 8,654

  8. Writing a Whole Number in Expanded Form The expanded form of a number shows each digit of the number with its place value.

  9. Example Write 804,557 in expanded form. 800,000 + 4000 + 500 + 50 + 7

  10. Reading Tables Tables are often used to organize and display facts that involve numbers.

  11. Example

  12. Example a. How many total Nobel Prize winners are from France? b. Which countries have more Nobel Prize winners than Germany? 58 Germany has 82, The United Kingdom has 110 and the United States has 320.

  13. Adding Whole Numbers and Perimeter 1.3

  14. Adding Whole Numbers, p 16 When the sum of digits in corresponding place values is more than 9, carrying is necessary. Example: 365 + 89 5 ones + 9 ones = 14 ones or 1 ten + 4 ones Write the 4 in the ones place and carry the 1 ten to the tens place. 1 ten + 6 tens + 8 tens = 15 tens or 1 hundred + 5 tens Write the 5 tens in the tens place and carry the 1 hundred to the hundreds place. Add the hundreds-place digits.

  15. Example, p 17 Add: 32,285 + 149,761 Practice Problem 2 Add: 27,364 + 92,977 120,341

  16. Adding Whole Numbers, p 17 Addition Property of 0 The sum of 0 and any number is that number. For example, 7 + 0 = 7 0 + 7 = 7

  17. Adding Whole Numbers, p 17 Commutative Property of Addition Changing the order of two addends does not change their sum. For example, 2 + 3 = 5 and 3 + 2 = 5.

  18. Adding Whole Numbers, p 18 Associative Property of Addition Changing the grouping of addends does not change their sum. For example, 3 + (5 + 7) = 3 + 12 = 15 and (3 + 5) + 7 = 8 + 7 = 15. Apply Practice 3 to the Commutative and Associative Properties

  19. Finding the Perimeter of a Polygon A polygon can be described as a flat figure formed by line segments connected at their ends. The perimeter of a polygon is the distance around the polygon. This means that the perimeter of a polygon is the sum of the lengths of its sides. P 18

  20. Example Find the perimeter of the polygon. 5 in 8 in 4 in 6 in 3 in To find the perimeter (distance around), we add the lengths of the sides. 5 in. + 8 in. + 6 in. + 3 in. + 4 in. = 26 in. P 19

  21. Solving Problems by Adding, p 19 P 19

  22. Solving Problems by Adding Example The state of Hawaii has 1851 miles of urban highways and 2291 miles of rural highways. Find the total highway mileage in Hawaii. (Source: U.S. Federal Highway Administration) P 20

  23. Subtracting Whole Numbers 1.4

  24. Subtracting Whole Numbers To subtract whole numbers, we subtract the digits in the ones place, then the tens place, then the hundreds place, and so on. Example: 7826 – 505 Line up numbers vertically so that the place values correspond. Then subtract the digits in corresponding place values, starting with the ones place. P 29

  25. Subtracting by Borrowing When subtracting vertically, if a digit in the second number (subtrahend) is larger than the corresponding digit in the first number (minuend), borrowing is necessary. P 30

  26. Subtracting Whole Numbers Example: 900 – 174 P 30

  27. Solving Problems by Subtracting P 31

  28. Solving Problems by Subtracting Example Dyllis King is reading a 503-page book. If she has just finished reading page 239, how many more pages must she read to finish the book? P 32

  29. Rounding and Estimating 1.5

  30. Rounding Whole Numbers Rounding a whole number means approximating it. 26 is closer to 30 than 20, so 26 is rounded to the nearest ten is 30. 52 is closer to 50 than 60, so 52 is rounded to the nearest ten is 50. P 39

  31. Rounding Whole Numbers 25 is halfway between 20 and 30. It is not closer to either number. In such a case, we round to the larger ten, that is, to 30. P 39

  32. Rounding Whole Numbers Round 32 to the nearest 10th Round 36 to the nearest 10th Round 35 to the nearest 10th Round to 30 Round to 40 Round to 40 Rounding Whole Numbers to a Given Place Value Step1: Locate the digit to the right of the given place value. Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and replace each digit to its right by 0. Step 3: If this digit is less than 5, replace it and each digit to its right by 0. P 39

  33. Examples 1. Round 568 to the nearest ten. 570 2. Round 278,362 to the nearest thousand. 278,000 3. Round 248,982 to the nearest hundred. 249,000 P 40

  34. Estimating Sums and Differences Estimate the sum by rounding each number to the nearest hundred. Example P 41

  35. Solving Problems by Estimating Example Jared Nuss scored 89, 92, 100, 67, 75 and 89 on his biology tests. Round each score to the nearest ten to estimate his total score. P 41

  36. DONE

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