1 NUMBERS BEYND 999 Let s recall... en ones (10 ones) en tens (10 tens) = = ne ten (1 ten) ne hundred (1 hundred) 1. Write the number names. (a) 287 (b) 199 (c) 304 (d) 888 2. Write 26 87 19 145 52 in ascending order. 3. Write 43 96 132 190 12 85 in descending order. 4. Sort out the following into even and odd numbers. 23 45 7 9 16 82 14 98 1 3 6 20 43 80 50 Even numbers dd numbers 5. Put the correct sign > < or = in the box. (a) 15 23 (b) 37 18 (c) 9 16 (d) 143 140 (e) 97 97 (f ) 75 216 1
6. Write in expanded form. (a) 538 = (b) 906 = 7. Write the number that comes before. (a) 399 (b) 870 (c) 473 8. Write the number that comes between. (a) 210 212 (b) 589 591 (c) 388 390 Let s learn further... en hundreds (10 hundreds) = ne thousand (1 thousand) 9 hundreds 9 tens 9 ones 900 90 9 = 999 999 is the greatest 3-digit number. Let s see what happens when we add one more to it. one more 2
9 hundreds (900) 10 tens (100) = 1 thousand (1000) 10 hundreds So 999 1 = 1000 = 1 thousand h 1 0 0 0 Remember We get 1000 which is the smallest 4-digit number. bserve the following pattern. n adding 1 to the largest 1-digit number we get the smallest 2-digit number. 9 1 = 10 n adding 1 to the largest 2-digit number we get the smallest 3-digit number. 99 1 = 100 n adding 1 to the largest 3-digit number we get the smallest 4-digit number. 999 1 = 1000 Counting by housands 1000 ne thousand 3
2000 wo thousand 3000 hree thousand 4000 Four thousand 5000 Five thousand 6000 Six thousand 7000 Seven thousand 4
8000 Eight thousand 9000 Nine thousand 10000 en thousand Numbers and Number Names Let s learn to form 4-digit numbers. Example 1: Represent the given 4-digit numbers in pictorial graphs and write their number names. (a) 1532 (b) 2645 (c) 9783 Solution: (a) 1532 (1 thousand) (5 hundreds) (3 tens) (2 ones) 1000 500 30 2 = 1532 It is read as one thousand five hundred thirty-two. 5
(b) 2645 (2 thousands) (6 hundreds) (4 tens) (5 ones) 2000 600 40 5 It is read as two thousand six hundred forty-five. = 2645 (c) 9783 (8 tens) (3 ones) 80 3 = 9783 It is read as nine thousand seven hundred eighty-three. (9 thousands) 9000 (7 hundreds) 700 We can also form 4-digit numbers using an abacus. Consider a 4-digit number 3285. We represent this on an abacus as shown. Remember h 3 2 8 5 hree thousand two hundred eighty-five 6
Example 2: Represent (a) 5064 (b) 7213 and (c) 9989 on the abacus. Solution: (a) 5064 (b) 7213 (c) 9989 h h h EXERCISE 1.1 1. Complete the following number grid. 1001 1011 1031 1002 1051 1081 1022 1023 1063 1014 1074 1045 1006 1075 1056 1027 1087 1018 1068 1039 1010 1030 1099 1060 1090 1100 2. bserve the pictorial blocks and write the number they represent. (a) = 7
(b) = = (c) 3. Draw beads to represent the following numbers on the abacus. (a) 1064 (b) 2731 h (d) 9890 8 h h h (f ) 5608 (e) 7342 h (c) 4576 h
4. Write the numbers represented on the abacus. (a) (b) (c) h h (d) h (e) (f ) h h h 5. Write the number names. (a) 3463 = (b) 7018 = (c) 9920 = (d) 5409 = (e) 6999 = Place Value and Face Value Mental Maths We know that the place value of a digit depends on its face value What is the place and its place or position in a number while the face value of a digit value and face value of 7 in 4706 is the value of the digit itself. As we move to the left the place value and in 7821? keep on increasing 10 times. Example 3: Write the place value and face value of digits in 8632. Solution: 8632 = 8 thousands 6 hundreds 3 tens 2 ones he place value of 8 in 8632 is 8000 and its face value is 8. he place value of 6 in 8632 is 600 and its face value is 6. he place value of 3 in 8632 is 30 and its face value is 3. he place value of 2 in 8632 is 2 and its face value is 2. 9
Expanded Form Example 4: Write 9516 in expanded form. Solution: 9516 = 9000 500 10 6 = 9 h 5 1 6 Expanded form of a number is the sum of the place values of its digits. Short form Expanded form EXERCISE 1.2 1. Fill in the boxes. (a) 3623 = h (b) 4780 = h (c) 6095 = h (d) 9909 = h 2. Write the number names in your notebooks. hen write their numbers. (a) 5 h 3 7 1 = (c) 4 h 9 2 4 = (e) 7 h 0 1 8 = (b) 6 h 8 0 2 = (d) 8 h 6 5 9 = (f) 3 h 5 0 3 = 3. Write in expanded form. (a) 1827 = (b) 9869 = (c) 8053 = (d) 5899 = 4. Write in short form. (a) 4000 300 10 9 = (c) 8000 400 60 1 = (b) 5000 700 80 6 = (d) 6000 0 90 8 = 10
5. Write the place value and face value of each circled digit of the given numbers in the table. Number 9 6 7 1 2 0 8 3 3 9 8 0 9 4 4 2 1 8 8 5 Place Value Face Value 6. Complete the sequence. (a) 2035 2039 (b) 3210 3215 (c) 5995 5998 (d) 9788 9792 Comparison of Numbers While comparing two numbers we must remember the following points: he number which comes later in counting is the bigger number. If two numbers have different number of digits then the number with more digits is always greater. Example 5: Compare the numbers 2685 and 798. Solution: he number of digits in 2685 = 4 and in 798 = 3. Since 4 > 3 therefore 2685 > 798. If two numbers have the same number of digits then always start comparing from the leftmost digit i.e. the digit at the thousands place in both the numbers. Example 6: Compare the numbers 2982 and 3105. Solution: he digit at the thousands place in 2982 is 2 and in 3105 is 3. Since 3 > 2 therefore 3105 > 2982. If the digits at the thousands place are same then compare the digits at the hundreds place. Example 7: Compare the numbers 4861 and 4539. Solution: he digit at the thousands place in both the numbers is 4. So we move ahead. he digit at the hundreds place in 4861 is 8 and in 4539 is 5. Since 8 > 5 therefore 4861 > 4539. If the digits at the thousands and hundreds place are same then compare the digits at the tens place. 11
Example 8: Compare the numbers 4861 and 4875. Solution: In both the numbers the digit at the thousands place is 4 and at the hundreds place is 8. he digit at the tens place in 4861 is 6 and in 4875 is 7. Since 7 > 6 therefore 4875 > 4861. If the digits at the thousands hundreds and tens place are same then compare the digits at the ones place. Example 9: Compare the numbers 4861 and 4865. Solution: In both the numbers the digits at the thousands place is 4 the hundreds place is 8 and the tens place is 6. he digit at the ones place in 4861 is 1 and in 4865 is 5. Since 5 > 1 therefore 4865 > 4861. If all the digits in both the numbers are same then the numbers are equal and we use the sign =. Mental Maths Which of these is greater? (a) 3291 286 (b) 5071 5312 (c) 6289 6298 (d) 7341 7340 Before After and Between he numbers which follow one after the other are called consecutive numbers. For example 1316 1317 1318 1319 1320 are consecutive numbers. Consecutive numbers can also be written backwards. For example 1320 1319 1318 1317 1316 A number one less than a given number comes just before it and is called its predecessor. A number one more than a given number comes just after it and is called its successor. Consider a 4-digit number 5863. Its predecessor = 5863 1 = 5862 and its successor = 5863 1 = 5864. 12
5862 5863 5864 predecessor is between 5862 and 5864 successor rdering of Numbers Comparison of two or more numbers becomes easy if we arrange the numbers in a sequence. his sequence can be from smaller to bigger or from bigger to smaller. Writing numbers in order from smaller to bigger is called ascending order and from bigger to smaller is called descending order. 6089 6190 7191 8792 are in ascending order. 9791 8790 7787 4688 are in descending order. Mental Maths Is 4271 4281 4396 4402 an ascending or descending sequence? EXERCISE 1.3 1. Put the correct sign < > or =. (a) 237 1201 (b) 3645 98 (c) 5421 5412 (d) 9781 9871 (e) 1212 1212 (f) 8064 7065 2. Arrange the following in ascending order. (a) 3285 4061 298 3469 (b) 1892 1982 1289 1189 (c) 9099 9909 9990 999 (d) 6341 6143 6431 6314 3. Arrange the following in descending order. (a) 7649 7496 7549 7459 (b) 8291 8192 8091 8129 (c) 1123 1312 1213 1321 (d) 4523 5619 4807 5032 4. Write the number that comes between the given numbers. (a) 698 700 (b) 4039 4041 (c) 1287 1289 (d) 8500 8502 13
5. Write the predecessor and successor of the given numbers. Predecessor Number Successor (a) 889 (b) 2341 (c) 7038 (d) 9000 6. Choose and write the largest number from the given numbers. (a) 3124 2689 708 4925 4259 (b) 1987 2000 2999 2001 399 (c) 6023 6203 6302 6320 6032 (d) 9989 9819 9899 9879 9897 Forming 4-digit Numbers We can form numbers using the given digits by arranging them in different order. For example using the digits 6 3 8 and 1 the greatest 4-digit number that can be formed is 8631 and the smallest 4-digit number that can be formed is 1368. 1. o form the greatest 4-digit number arrange the given digits in descending order. 2. o form the smallest 4-digit number arrange the given non-zero digits in ascending order. Example 10: Write the greatest and the smallest 4-digit number using the digits 2 9 0 and 5. Solution: he greatest 4-digit number is 9520. (on arranging the digits in descending order) he smallest 4-digit number is 2059. (on arranging the digits in ascending order) Note that the smallest 4-digit number is 2059 and not 0259 as 0 in the beginning of a number has no value. Skip Counting You have already learnt skip counting in 2 s 3 s 5 s and 10 s in the previous class. Now let s learn skip counting in 100 s and 1000 s. 14 Remember
Skip count in 100 s means skipping 100 places (digits at the tens and ones places remain the same). For example 7108 7208 7308 7408 7508 Skip count in 1000 s means skipping 1000 places (digits at the hundreds tens and ones places remain the same). For example 2845 3845 4845 5845 6845 7845 More han and Less han Consider the number 8135. o find a number 2 more than 8135 we add 2 to 8135 i.e. 8135 2 = 8137. o find a number 3 less than 8135 we subtract 3 from 8135 i.e. 8135 3 = 8132. You need not add or subtract every time. You can also observe the pattern and find the number. Mental Maths What is 10 more than 90? What is 10 less than 50? EXERCISE 1.4 1. Build the greatest and the smallest number with the given digits using each digit only once. Digits Greatest Number Smallest Number (a) 3 8 2 1 (b) 5 6 0 3 (c) 9 5 8 7 (d) 0 2 4 6 2. Skip count in 100 s and complete the pattern. (a) 4531 4631 (b) 5287 5387 (c) 1872 1972 (d) 6594 6694 15
3. Skip count in 1000 s and complete the pattern. (a) 1045 2045 (b) 3986 4986 (c) 2105 3105 (d) 4999 5999 4. Match the following. Column A Column B (a) (b) (c) (d) (e) (f ) (g) (h) 4 more than 2096 10 more than 8285 1 less than 4000 10 less than 9989 100 more than 7685 100 less than 3175 1000 more than 5893 1000 less than 6940 (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) 3999 7785 2100 3075 8295 5940 6893 9979 Rounding ff Numbers ey friends can you guess the number of ice creams in the cart? mm... about 50 or 60! When we are not sure of the exact number we use the word about. It gives a rough estimation of the number. We can also say that the number has been rounded off. We can round off a number to the nearest 10 100 or 1000. Rounding off to the nearest 10 o round off a number to the nearest ten look at the digit in the ones place. If the digit in the ones place is 4 or less then place a zero in the ones place and let the digit in the tens place remain as it is. If the digit in the ones place is 5 or more then place a zero in the ones place. Also add 1 to the digit in the tens place. 16
Example 11: Round off (a) 43 (b) 87 and (c) 65 to the nearest 10. Solution: (a) 43 is rounded off to 40 since the digit in the ones place is 3 which is less than 5. (b) 87 is rounded off to 90 since the digit in Mental Maths the ones place is 7 which is more than 5. Round off to the nearest 10. (c) 65 is rounded off to 70 since the digit in (a) 68 (b) 82 the ones place is 5. Rounding off to the nearest 100 o round off a number to the nearest hundred look at the digit in the tens place. If the digit in the tens place is 4 or less then place zeros in the tens and ones place. he digit in the hundreds place remains the same. If the digit in the tens place is 5 or more then place zeros in the tens and ones place. Add 1 to the digit in the hundreds place. Example 12: Round off (a) 243 and (b) 1887 to the nearest 100. Solution: (a) 243 is rounded off to 200 because the digit at the tens place is 4. (b) 1887 is rounded off to 1900 because the digit at the tens place is 8. (c) 94 (d) 55 Mental Maths Round off to the nearest 100. (a) 497 (b) 8383 Rounding off to the nearest 1000 (c) 216 (d) 3541 o round off a number to the nearest thousand look at the digit in the hundreds place. If the digit in the hundreds place is 4 or less then place zeros in the digits at the hundreds tens and ones place. Keep the digit in the thousands place as it is. If the digit in the hundreds place is 5 or more then place zeros in the digits at the hundreds tens and ones place. Also add 1 to the digit in the thousands place. Example 13: Round off (a) 6253 and (b) 7923 to the nearest 1000. Solution: (a) 6253 is rounded off to 6000 as the digit in the hundreds place is 2. (b) 7923 is rounded off to 8000 as the digit in the hundreds place is 9. Mental Maths Round off to the nearest 1000. (a) 7249 (b) 1621 (c) 5913 (d) 8469 Even and dd Numbers You have already studied that numbers which can be put in pairs are called even numbers and numbers which cannot be put in pairs are called odd numbers. For example 238 1746 3280 7632 are even numbers and 413 685 7981 9377 are odd numbers. 17
o decide whether a given number is even or odd we look at the ones place. If the digit in the ones place is 0 2 4 6 or 8 then the number is an even number. If the digit in the ones place is 1 3 5 7 or 9 then the number is an odd number. EXERCISE 1.5 1. Round off the following numbers to the nearest 10. (a) 63 (b) 922 (c) 35 2. Round off the following numbers to the nearest 100. (a) 586 (b) 354 (c) 1177 3. Round off the following numbers to the nearest 1000. (a) 6119 (b) 7999 (c) 2534 4. Match the following. Number Rounded off to the nearest 10 (a) 94 (i) 50 (b) 11 (ii) 100 (c) 46 (iii) 70 (d) 68 (iv) 10 (e) 95 (v) 90 5. Separate and write the even and odd numbers into their respective boxes. 46 83 175 220 1643 2040 9891 687 1849 7514 6322 9295 5040 4783 Even numbers dd numbers LE S EVALUAE 1. bserve the pictorial blocks and write the numbers they represent. (a) = 18
(b) = 2. Draw beads to represent the numbers given in the boxes. (a) (b) (c) h h h 3628 5907 9021 3. Fill in the boxes. (a) 7982 = h (b) 2805 = h (c) (d) = 6 h 0 1 9 = 8 h 9 2 7 4. Write in expanded form. (a) 4208 = (b) 8976 = (c) 1635 = 5. Write the place value of the circled digit in the given numbers. (a) 4 3 2 7 (b) 8 5 0 1 6. Write five consecutive numbers for the given numbers. (a) 3186 (b) 9247 19
7. Put the correct sign < > or =. (a) 2531 1235 (b) 1607 1507 (c) 9875 9872 (d) 2304 2430 (e) 6287 6293 (f) 3195 3195 8. Arrange 5624 5426 4571 6245 6345 6340 in ascending order. 9. Arrange 1843 1934 1624 1857 1846 1924 in descending order. 10. Colour the largest number blue and the smallest number pink. (a) 9003 9130 9821 9128 9009 9812 (b) 5613 5420 5375 5289 5280 5614 11. Write rue or False. (a) he predecessor of 2090 is 2091. (b) 4896 is an even number. (c) he successor of 7819 is 7820. (d) 2437 lies in between 2435 and 2436. (e) 62 rounded off to its nearest 10 is 70. (f) In words 9038 is written as nine thousand thirty-eight. 12. Write five numbers backward from the given numbers. (a) 5643 (b) 9289 13. here are 2015 students in a school. Write the number of students in words. 14. A school X has 1986 students and another school Y has 1896 students. Which school has more students? 15. here were 163 people in a party. What is the estimate (to the nearest 10) of the number of people in the party? 16. In a game Rima picked up four digits from a bowl containing digits from 0 to 9. he digits she picked up were 3 5 6 and 8. What is the greatest number that Rima could make using these digits? 20
17. Choose the correct answer. (a) he place value of 7 in 8375 is: (i) 700 (ii) 7000 (iii) 70 (ii) 8502 (iii) 8508 (b) 8503 is greater than: (i) 9846 (c) he greatest 4-digit number formed using 4 5 3 0 is: (i) 5430 (ii) 5304 (iii) 5403 (d) he smallest 4-digit number formed using 9 7 2 0 is: (i) 0972 (e) 6 less than 9442 is: (i) 9346 (ii) 2079 (iii) 2097 (ii) 9446 (iii) 9436 VALUES AND LIFE SKILLS Write the number names of the numbers represented on the abacus. (a) (b) h h Do you think abacus helps you to understand numbers better? In what all ways does it help you? SCRAC YUR BRAIN (S) 1. What is the difference between the largest 3-digit number and the smallest 2-digit number? 2. 4087 stands for RANK 5128 stands for SUN and 9073 stands for CAKE. What do the following numbers stand for? (a) 5904 (b) 1248 (c) 1307 (d) 4381 21
Colour and Learn 5369 36 1023 00 19 9443 9999 70 40 77 21 80 1000 2684 22 24 54 90 6319 9301 3825 5686 1120 2892 1. Colour the smallest 4-digit number green. 2. Colour the largest 4-digit number orange. 3. Colour the numbers which are the predecessors of the following numbers red. (a) 5370 (b) 1121 4. Colour the numbers which are the successors of the following numbers yellow. (a) 2891 (b) 9300 5. Colour the even numbers pink. 6. Colour the odd numbers purple. MAS LAB ACIVIY 1. Cut a big cardboard in the shape of a circle. 2. Now cut 10 small circles of different coloured sheets of paper and mark them as 0 1 2 3 4 5 6 7 8 9. 3. Paste these small numbered circles on the cardboard in a mixed order. 4. ang the cardboard on the wall. 5. Each child should come one by one and hit the cardboard with a small plastic ball till four numbers are hit. 6. Each time the child hits a digit he/she should note it down. hus every child will have 4 digits. 7. Using the 4 digits each child should form the following and write their number names. (a) the greatest 4-digit number (b) the smallest 4-digit number (c) as many 4-digit numbers as possible 22