Class notes Math 120

Specific Objectives By the end of the topic the learner should be able to: a.) Identify, read and write natural numbers in symbols and words; b.) Round off numbers to the nearest tens, hundreds, thousands, millions and billions; c.) Classify natural numbers as even, odd or prime; d.) Solve word problems involving natural numbers. Content a.) Place values of numbers b.) Rounding off numbers to the nearest tens, hundreds, thousands, millions and billions c.) Odd numbers d.) Even numbers e.) Prime numbers f.) Word problems involving natural numbers Introduction Place value A digit have a different value in a number because of its position in a number. The position of a digit in a number is called its place value. Total value This is the product of the digit and its place value. Example Number Hundred Millions Ten Millions Millions Hundred Thousands Ten Thousands Thousands Hundred Tens ones 345,678,901 3 4 5 6 7 8 9 0 1 769,301,854 7 6 9 3 0 1 8 5 4 902,350,409 9 0 2 3 5 0 4 0 9 NATURAL NUMBERS 8 WWW.TEACHER.CO.KE A place value chart can be used to identify both place value and total value of a digit in a number. The place value chart is also used in writing numbers in words. Example Three hundred and forty five million, six hundred and seventy eight thousand, nine hundred and one. Seven hundred and sixty nine million, Three hundred and one thousand, eight hundred and fifty four. Billions A billion is one thousands million, written as 1, 000, 000,000.There are ten places in a billion. Example What is the place value and total value of the digits below? a.) 47,397,263,402 (place value 7 and 8). b.) 389,410 ,000,245 ( place 3 and 9) Solution a.) The place value for 6 is ten thousands. Its total value is 60,000. b.) The place value of 3 is hundred billions. Its total value is 300,000,000,000. Rounding off When rounding off to the nearest ten, the ones digit determines the ten i.e. if the ones digit is 1, 2, 3, or 4 the nearest ten is the ten number being considered. If the ones digit is 5 or more the nearest ten is the next ten or rounded up. Thus 641 to the nearest ten is 640, 3189 to the nearest is 3190. When rounding off to the nearest 100, then the last two digits or numbers end with 1 to 49 round off downwards. Number ending with 50 to 99 are rounded up. Thus 641 to the nearest hundred is 600, 3189 is 3200. Example Rounding off each of the following numbers to the nearest number indicated in the bracket: a.) 473,678 ( 100) b.) 524,239 (1000) c.) 2,499 (10) Solution a.) 473,678 is 473,700 to the nearest 100. b.) 524,239 is 524,000 to the nearest 1000 c.) 2,499 is 2500 to the nearest 10. 9 WWW.TEACHER.CO.KE Operations on whole Numbers Addition Example Find out: a.) 98 + 6734 + 348 b.) 6349 + 259 +7954 Solution Arrange the numbers in vertical forms 98 6734 + 348 7180 634