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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Prealgebra Section 1.1: Whole Numbers and Rounding

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Objectives o Learn to read and write whole numbers. o Know that the word and is not used when reading or writing whole numbers. (And is used to indicate a decimal point.) o Learn how to round whole numbers to a given place.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 1: Reading and Writing Whole Numbers The whole numbers are the natural (or counting) numbers and the number 0. Natural numbers = = {1,2,3,4,5,6,7,8,9,10,11,…} Whole numbers = = {0,1,2,3,4,5,6,7,8,9,10,11,…} Note that 0 is a whole number but not a natural number. The three dots (called an ellipsis) in the definition indicate that the pattern continues without end.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 1: Reading and Writing Whole Numbers (cont.) To write a whole number in standard notation (or standard form) we use a place value system that depends on three things: 1.the tens digit: 0,1,2,3,4,5,6,7,8,9; 2.the placement of each digit; and 3.the value of each place.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. The figure below shows the value of the first ten places in the decimal system we use. Every three places constitutes a period and the digits in each period are separated with commas. A number with 4 or fewer digits need not have any commas. Obj 1: Reading and Writing Whole Numbers (cont.)

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. To read (or write) a number in this system, start from the left and use the name of the number (three digits or less) in each period. For example, 7,839,076,532 is read as: seven billion, eight hundred thirty-nine million, seventy-six thousand, five hundred thirty-two. (Note that a hyphen is used when writing two-digit numbers larger than twenty). Obj 1: Reading and Writing Whole Numbers (cont.)

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 2: The Word “And” Note that the word and does not appear as part of reading (or writing) any whole number. The word and indicates the decimal point. You may put a decimal point to the right of the digits in a whole number if you choose, but it is not necessary unless digits are written to the right of the decimal point.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Writing Whole Numbers The following numbers are written in standard notation. Write them in their English word equivalent. a. 25,380 twenty-five thousand, three hundred eighty b.3,400,562 three million, four hundred thousand, five hundred sixty-two

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 1: Writing Whole Numbers The following numbers are written in standard notation. Write them in their English word equivalent. a.32,450,090 thirty-two million, four hundred fifty thousand, ninety b.5784 five thousand seven hundred eighty-four

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Writing Whole Numbers The following numbers are written in words. Rewrite them in standard notation. a. twenty-seven thousand, three hundred thirty-six 27,336 b.three hundred forty million, sixty-two thousand, forty-eight 340,062,048 (Note how 0’s must be used to fill out a three-digit period.)

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 2: Writing Whole Numbers The following numbers are written in words. Rewrite them in standard notation. a.six thousand forty-one 6041 b.nine billion, four hundred eighty-three thousand 9,000,483,000

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Rounding Whole Numbers To round a given number means to find another number close to the given number. The desired place of accuracy must be stated. For example, if you were asked to round 762, you might say 760 or 800. Either answer could be correct, depending on whether the accuracy was to be the nearest ten or the nearest hundred. Rounded numbers are quite common and acceptable in many situations.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Rounding Whole Numbers (cont.) For example, a credit card application might ask for your approximate income: 0 - $10,000, $10,001 - $20,000, $20,001 - $30,000, $30,001 - $40,000, and so on, but not your exact income. Even the IRS allows rounding to the nearest dollar when calculating income tax. In effect, rounded numbers are simply approximations of the given numbers.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Rounding Whole Numbers (cont.) In the following examples we use number lines as visual aids in understanding the rounding process. On number lines the whole numbers are used to label equally spaced points, usually to the right of the point labeled 0.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Rounding Whole Numbers Round 762 a.to the nearest ten. We see that 762 is closer to 760 than to 770. Thus 762 rounds to 760 (to the nearest ten).

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Rounding Whole Numbers (cont.) Round 762 b.to the nearest hundred. Also, 762 is closer to 800 than to 700. Thus 762 rounds to 800 (to the nearest hundred).

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 3: Rounding Whole Numbers Use a number line to round each number as indicated. a.583 (to the nearest ten) b.269 (to the nearest hundred) c.9732 (to the nearest thousand) d.9732 (to the nearest hundred) 580 300 10,000 9700

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Obj 3: Rounding Whole Numbers (cont.) Rounding Rule for Whole Numbers 1.Look at the single digit just to the right of the digit that is in the place of desired accuracy. 2.If this digit is 5 or greater, make the digit in the desired place of accuracy one larger and replace all digits to the right with zeros. All digits to the left remain unchanged unless a 9 is made one larger; then the next digit to the left is increased by 1. 3.If this digit is less than 5, leave the digit that is in the place of desired accuracy as it is, and replace all digits to the right with zeros. All digits to the left remain unchanged.

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Round each number as indicated: a.6849 (nearest hundred) Example 4: Rounding Whole Numbers 6849 Place of desired accuracyLook at one digit to the right; 4 is less than 5. 6800 Leave 8 and fill in zeros. So, 6849 rounds to 6800 (to the nearest hundred).

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Round each number as indicated: b.3500 (nearest thousand) Example 4: Rounding Whole Numbers (cont.) 3500 Place of desired accuracyLook at 5; 5 is 5 or greater.Increase 3 to 4 (one larger) and fill in zeros. 4000 So, 3500 rounds to 4000 (to the nearest thousand).

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 4: Rounding Whole Numbers (cont.) Round each number as indicated: c.597 (nearest ten) 597600 Place of desired accuracy.Look at 7; 7 is greater than 5.Increase 9 to 10. (This affects two digits, both 5 and 9.) So, 597 rounds to 600 (to the nearest ten).

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HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Self-Check 4: Rounding Whole Numbers Round each number as indicated: a. 7350 (nearest hundred) b. 29,736 (to the nearest thousand) c. 137,800 (to the nearest hundred thousand) d. 28,379,200 (to the nearest million) 30,000 7400 100,000 28,000,000

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