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Objectives A. To identify the order relation between two numbers B. To write whole numbers in words and in standard form C. To write whole numbers in expanded form D. To round a whole number to a given place value 3

OBJECTIVE A To identify the order relation between two numbers 4

To identify the order relation between two numbers The whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,.... The three dots mean that the list continues on and on and that there is no largest whole number. Just as distances are associated with the markings on the edge of a ruler, the whole numbers can be associated with points on a line. This line is called the number line. 5

To identify the order relation between two numbers The arrow on the number line below indicates that there is no largest whole number. The graph of a whole number is shown by placing a heavy dot directly above that number on the number line. Here is the graph of 7 on the number line: 6

To identify the order relation between two numbers The number line can be used to show the order of whole numbers. A number that appears to the left of a given number is less than (<) the given number. A number that appears to the right of a given number is greater than (>) the given number. Four is less than seven. 4 < 7 Twelve is greater than seven. 12 > 7 7

Example 2 Place the correct symbol, < or >, between the two numbers. a. 39 24 b. 0 51 Solution: a. 39 > 24 b. 0 < 51 8

OBJECTIVE B To write whole numbers in words and in standard form 9

To write whole numbers in words and in standard form When a whole number is written using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, it is said to be in standard form. The position of each digit in the number determines the digit s place value. The diagram below shows a place-value chart naming the first 12 place values. The number 37,462 is in standard form and has been entered in the chart. 10

To write whole numbers in words and in standard form In the number 37,462, the position of the digit 3 determines that its place value is ten-thousands. When a number is written in standard form, each group of digits separated from the other digits by a comma (or commas) is called a period. The number 3,786,451,294 has four periods. The period names are shown in red in the place-value chart. 11

To write whole numbers in words and in standard form To write a number in words, start from the left. Name the number in each period. Then write the period name in place of the comma. 3,786,451,294 is read three billion seven hundred eighty-six million four hundred fifty-one thousand two hundred ninety-four. 12

To write whole numbers in words and in standard form To write a whole number in standard form, write the number named in each period, and replace each period name with a comma. Four million sixty-two thousand five hundred eighty-four is written 4,062,584. The zero is used as a place holder for the hundred-thousands place. 13

Example 3 Write 25,478,083 in words. Solution: Twenty-five million four hundred seventy-eight thousand eighty-three 14

OBJECTIVE C To write whole numbers in expanded form 15

To write whole numbers in expanded form The whole number 26,429 can be written in expanded form as 20,000 + 6000 + 400 + 20 + 9. The place-value chart can be used to find the expanded form of a number. 16

To write whole numbers in expanded form The number 420,806 is written in expanded form below. Note the effect of having zeros in the number. or simply 400,000 + 20,000 + 800 + 6. 17

Example 5 Write 23,859 in expanded form. Solution: 20,000 + 3000 + 800 + 50 + 9 18

OBJECTIVE D To round a whole number to a given place value 19

To round a whole number to a given place value When the distance to the moon is given as 240,000 miles, the number represents an approximation to the true distance. Taking an approximate value for an exact number is called rounding. A rounded number is always rounded to a given place value. 20

To round a whole number to a given place value 37 is closer to 40 than it is to 30. 37 rounded to the nearest ten is 40. 673 rounded to the nearest ten is 670. 673 rounded to the nearest hundred is 700. 21

To round a whole number to a given place value How To Round 13,834 to the nearest hundred. If the digit to the right of the given place value is less than 5, that digit and all digits to the right are replaced by zeros. 13,834 rounded to the nearest hundred is 13,800. 22

Example 7 Round 525,453 to the nearest ten-thousand. Solution: 525,453 rounded to the nearest ten-thousand is 530,000. 23