In our number system, we can write any number using a combination of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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1 10 WHOLE NUMBERS (Chapter 1) Opening problem The scorecard alongside shows the number of runs scored by each batsman in an innings of cricket. Things to think about: a How many batsmen scored: i less than 10 runs ii 100 runs or more? b We sometimes say that batsmen who have scored 100 runs or more have reached triple figures. Can you explain what this means? c How many runs did Jones and Williams score in total? d How many more runs did Stone score than Mullner? F. JONES C. WILLIAMS T. CHURCH A. THOMSON G. MULLNER S. STONE W. HIGGINS L. SPENCER T. HILL P. SPIERS M. HAINES EXTRAS TOTAL 563 In our number system, we can write any number using a combination of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, the number fifty seven can be written using the digits 5 and 7 as 57. The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,... and so on are known as the whole numbers. In this chapter, we will learn about writing, rounding, adding, and subtracting whole numbers. A The place or position of a digit in a number determines its value. PLACE VALUE units 1 tens 10 hundreds 100 thousands 1000 ten thousands hundred thousands

2 WHOLE NUMBERS (Chapter 1) 11 The number 5382 is a short way of writing thousands + 3 hundreds + 8 tens + 2 units thousands hundreds tens units We write 5382 in words as five thousand, three hundred, and eighty two. In some numbers, we use the digit zero or 0 to show an empty place value. For example: ² 5206 is or five thousand, two hundred, and six. 0 shows there are no tens ² 7640 is or seven thousand, six hundred, and forty. 0 shows there are no units Historical note An abacus or counting frame is a tool used to perform operations with numbers. It was invented over 4300 years ago in Mesopotamia, which is in modern-day Iraq. The abacus is still used by traders in Asia and Africa. EXERCISE 1A 1 Write each of the following numbers in short form: a b c d e f g h i j Write each of the numbers in 1 in words. 3 Write as a number in short form: a five thousand, seven hundred, and forty four b two thousand, nine hundred, and eleven c eight thousand and eight d fifteen thousand, two hundred, and thirty seven e twenty four thousand, six hundred, and one f eighty eight thousand, eight hundred g four hundred and seventy two thousand, six hundred, and seventeen

3 12 WHOLE NUMBERS (Chapter 1) 4 Match each number with its value: a 527 b 28 c 3073 d 208 e 5207 f 373 g 5027 h 3730 A B C D E F G H Example 1 What number does this abacus show? The number of disks on each spike represents the digit for that position. We count the number of disks on each spike The abacus shows the number What number does each abacus show? hundred thousands ten thousands thousands hundreds tens units DEMO a b c d e f

4 WHOLE NUMBERS (Chapter 1) 13 g h i 6 Draw an abacus to show each of the following numbers: a 3617 b 5088 c d Example 2 What number is represented by the digit 5 in: a 251 b 4205 c ? a In 251, the 5 represents 5 tens, or 50. b In 4205, the 5 represents 5 units, or 5. c In , the 5 represents 5 ten thousands, or What number is represented by the digit 6 in: a 657 b 8617 c 168 d 4962 e 3076 f 6294 g h ? 8 What number is represented by the digit 3 in: a 903 b 1302 c 238 d 3888 e 7030 f g h ? 9 For the number , write down the value of the: a 6 b 1 c 3 d 7 e 8 10 For the number , write down the value of the: a 9 b 1 c 4 d 7 e 5 Example 3 Arrange in order from smallest to largest: 24, 42, 27, 72, 47 All of the numbers have two digits. In each number we look first at the number of tens, and then at the number of units. 24 and 27 have the smallest number of tens, and 24 has less units so it is smallest. 42 and 47 have the same number of tens, and 42 has less units than has the most number of tens, so it is the largest number. So, in order from smallest to largest, we have: 24, 27, 42, 47, 72.

5 14 WHOLE NUMBERS (Chapter 1) 11 Arrange each set of numbers in order from smallest to largest: a 39, 93, 19, 31, 91 b 308, 301, 207, 109, 208 c 2710, 2071, 2701, 2017, 2170 d , , , , e f sixty four, forty, sixteen, forty six, sixty, fourteen seventeen, seventy, fifty seven, seventy five, fifteen g one thousand and fifty three, 1503, one thousand and fifty, 1305 h two thousand and forty seven, 2407, 247, seven hundred and twenty four. 12 Write down the largest and smallest numbers we can make using the digits: It may be helpful to use a place value table. a 4, 2, 9, and 3 b 8, 3, 5, 2, and 9 c 3, 8, 6, 7, and 4. B ROUNDING NUMBERS When a quantity is being described, we often do not need to know the exact number. For example: ² You may look at a handful of marbles and say, There are about thirty there. ² A fishing report might read About 600 kg of crayfish were caught last week. ² A commentator might estimate the crowd at a sporting event as When we estimate a number of objects, we usually round to the nearest 10, 100, 1000, and so on. There are rules for doing this. ROUNDING TO THE NEAREST TEN This number line shows the whole numbers from 20 to 30. nearer to 20 nearer to , 22, 23, and 24 are nearer to 20 than to 30, sowe round them down to , 27, 28, and 29 are nearer to 30 than to 20, sowe round them up to is midway between 20 and 30 on the number line. We make the choice that numbers ending in 5 will be rounded up to the next 10. So, 25 is rounded up to 30.

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