NOTATION AND WHOLE NUMBERS Value and Place Value  Digits are symbols used to write numerals; 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the digits used in our number system. The number 2 345 689 has 7 digits. In words it is: two million, three hundred and forty-five thousands, six hundred and eighty-nine.  The "place value" of each digit in 2 345 689 is as follows:The 2 is in the millions place. The 3 is in the hundred thousands place. The 4 is in the ten thousands place. The 5 is in the thousands place. The 6 is in the hundreds place. The 8 is in the tens place. The 9 is in the ones place. The "value" of each digit in 2 345 689 is as follows: The 2 stands for 2 000 000 or 2 millions. The 3 stands for     300 000 or 3 hundred thousands. The 4 stands for      40 000 or 4 ten thousands. The 5 stands for       5 000 or 5 thousands. The 6 stands for          600 or 6 hundreds. The 8 stands for             80 or 8 tens. The 9 stands for               9 or 9 ones.     Symbols < is greater than > is greater than = is equal to  ~ approximately equal to Sequences A number sequence is a set of numbers in which each number follows the last one according to some rule or pattern.   Examples:  422, 424, 426, 428 …. are even numbers. Rule: Start with 422 and add 2 each time. 3 206, 3 203, 3 200, 3 197, 3 194 … Rule: Start with 3 206 and subtract 3 each time.   Factors A factor is a number that is multiplied by another number to give a product. In 2x5 = 10, 2 and 5 are the factors. When we multiply 2 by 5, we get a product of 10.   Multiples A multiple of a number is the product of that number and a whole number. 0, 8, 16, 24, 32, 40 and so on are multiples of 8.  Rounding Rounding off a number to a specified place value means naming the multiple of a place value to which the number is closest. Example: Round off 42 083 to the nearest ten. 42 083 is greater than 42 080 and less than 42 090. It is closer to 42 080. When a number is halfway between such as 42 085, it is rounded off to 42 090. The Four Operations of Whole Numbers Do what is in the bracket first. Example: (36 + 18) x 2 = 54 x 2 = 108 When a mathematical expression without brackets involves mulitplication and division only, we work from left to right. Example: 80 ÷ 2 x 3  = 40 x 3 = 120 When a mathematical expression without brackets involves addition and subtraction only, we work from left to right.   Example: 105 – 95 + 16 = 10 + 16 = 26 When a mathematical expression involves several numbers and operations, we work in this way:  Do the operation in the brackets first. Do the multiplication and division from left to right. Then do addition and subtraction from left to right. Example: 12 + 14 ÷ (11 – 4) x 6 – 16 = 12 + 14 ÷7 x 6 – 16 = 12 + 2 x 6 – 16  = 12 + 12 – 16 = 24 – 16 = 8   Problem Solving Guide Carefully read the problem. Identify the important data, information and key words. Make a plan. Work it out. Check the working and statements. Example: Andy has twice as much money as Bob. Bob has \$8.50 and Charles has three times as much as Andy and Bob have altogether. How much money do they have altogether?     2 x \$8.50 = \$17.00 Andy has \$17.00 ………………………………………….. (a) (\$8.50 + \$17.00) x 3 = \$76.50 Charles has \$76.50 ………………………………………… (b) \$8.50 + 417.00 + \$76.50 = \$102.00 They have \$102.00 altogether ……………………………... (c)