Large numbers

Large number grade 5
CBSE

1. Large Numbers Grade 5 Nisha Mahajan

2. Topics Covered Place Value – Value of a number according to it Place Face Value – Absolute value of a number i.e. Digit. Indian Place Value system International Place Value System 8 digit number Numeration of a number - Indian and International place value Long Expanded form Short Expanded form Standard form

3. Place Value Q . Write the place value of 2 in: a) 5428 b) 7246 Th H T O Th H T O 5 4 2 8 7 2 4 6 Ans . 20 Ans. 200

4. Indian Place Value International Place Value

5. Standard Form – 8 digit Crores Lakhs Thousands Ones T Cr Cr T L L T Th Th H T O 5 4 2 8 7 2 4 6 Millions Thousands Ones H M T M M H Th T Th Th H T O 5 4 2 8 7 2 4 6 Indian Place Value System International Place Value System Solution – 5,42,87,246 Solution – 54,287,246

6. Word Numeration/Number names – 8 digit 54,287,246 Fifty four millions two hundred eighty seven thousands two hundred and forty six Millions Thousands Ones H M T M M H Th T Th Th H T O 100,000,000 10,000,000 1,000,000 100,000 10,000 1000 100 10 1 5 4 2 8 7 2 4 6

7. Expanded Form – 8 digit 54,287,246 Long Expanded Form ( 5 x 10,000,000 ) + ( 4 x 1,000,000 ) + ( 2 x 100,000 ) + ( 8 x 10,000 ) + ( 7 x 1000 ) . + ( 2 x 100 ) + ( 4 x 10 ) + ( 6 x 1 ) Short Expanded Form 50,000,000 + 4,000,000 + 200,000 + 80,000 + 7,000 + 2000 + 40 + 6 Millions Thousands Ones H M T M M H Th T Th Th H T O 100,000,000 10,000,000 1,000,000 100,000 10,000 1000 100 10 1 5 4 2 8 7 2 4 6

8. Expanded Form – 9 digit 154287246 Standard Form 154,287,246 Word/Number Name : One hundred fifty four millions two hundred eighty seven thousands two hundred and forty six Long Expanded Form ( 1 x 100,000,000 ) + ( 5 x 10,000,000 ) + ( 4 x 1,000,000 ) + ( 2 x 100,000 ) + ( 8 x 10,000 ) + ( 7 x 1000 ) + ( 2 x 100 ) + ( 4 x 10 ) + ( 6 x 1 ) Short Expanded Form 100,000,000 + 50,000,000 + 4,000,000 + 200,000 + 80,000 + 7,000 + 2000 + 40 + 6 Millions Thousands Ones H M T M M H Th T Th Th H T O 100,000,000 10,000,000 1,000,000 100,000 10,000 1000 100 10 1 1 5 4 2 8 7 2 4 6

9. Largest and Smallest number Smallest 8 digit number – 10,000,000 Largest 8 digit number – 99,999,999 Smallest 9 digit number – 100,000,000 Largest 9 digit number – 999,999,999 Fun Fact Largest n digit number + 1 = smallest n+1 digit number Eg. largest 8 digit number = smallest 9 digit number i.e. 99,999,999 + 1 = 100,000,000

10. Building greatest and smallest numbers To get greatest number , we arrange the digits in descending order. Eg. 7 ,2, 0 , 1 , 8 , 3 , 4 8 7 4 3 2 1 0 To get the smallest number , we arrange the digit in ascending order. ( we do not place 0 at extreme left ) Eg. 7 ,2, 0 , 1 , 8 , 3 , 4 1 0 2 3 4 7 8

11. Homework Write the following in place value chart: a) 48374951 b) 200091386 c) 165329814 Write the following numbers in standard form and in words: a) 325102014 b) 700000008 c) 6839205 Write the following numbers in short expanded form: a) 47392469 b) 789542370 Write the Successor of Greatest 7 digit number Smallest 6 digit number

12. Homework Write the Successor of Smallest 9 digit number Greatest 8 digit number Write the greatest and smallest 7 digit number using ( without repeating the digits) 4, 7 , 6 , 3 , 2 , 9 and 1 B) 2, 5 , 6 , 0 , 4 , 3 and 7 Find place value of a) 2 in 523,567,986 b) 1 in 170,364 c) 7 in 876,892,046 Write the following number in figures a) Three hundred fifteen thousand , four hundred nineteen b) Thirty two million four hundred seventy five thousand four

13. Successor Successor of number is one more than the number. Eg. 567,892,876 Successor – 567,892,876 + 1 = 567,892,877 Predecessor Predecessor of number is one less than the number. Eg. 567,892,876 Successor – 567,892,876 - 1 = 567,892,875 Fun Fact – Successor of Largest n digit number + 1 = smallest n+1 digit number Eg. Successor of largest 6 digit number = smallest 7 digit number i.e. 999,999 + 1 = 1,000,000

14. Conversion 70 X ______ = 7 Million 70 x _____ = 7,000,000 4 Thousand X ______ = 400 Million 4000 x _____ = 400,000,000 7 Hundred X ______ = 700 Million 700 x _____ = 700,000,000 Millions Thousands Ones H M T M M H Th T Th Th H T O 100,000,000 10,000,000 1,000,000 100,000 10,000 1000 100 10 1

15. Comparing large number Number with more digit is greater . Eg. 76,089,364 > 9,735,367 If both numbers have equal no. of digits, then the number with the greatest digit in largest place is greater. Eg . 7 6,089,364 < 9 8,735,367 76,09 8 ,653 < 76,09 9 ,763

16. Practice Find the successor of : 9,825,799 19,999,999 Greatest 7 digit number Find the predecessor of 73,500,000 98,563,110 Smallest 8 digit number Write the greatest and the smallest 6 digit number , without repetition 2 , 9 , 3 , 6 , 1 , 5 7 , 2 , 8 , 0 , 1 , 1

17. Practice Complete the pattern 534,027 , 534,127 , 534,227, _______, _______, ______. 4,312,563, 4,322,563, 4,332,563, _______, ______, _______. Compare 357,412 _____ 1,541,378 35,192,570 _____31,927,053 87,378,839 _____ 87,378,840 927,278 _____ 927,179

18. Rounding off number nearest 10 We replace the digit in ones place by 0. If the unit or ones place is > 5 , we increase the digit in tens place by 1 else make no change. Eg. 254 6 Here 6 > 5 , there for we will replace ones place i.e. 6 by 0 and increase tens place digit i.e. 4 by 1 Ans – 25 50 Eg. 254 3 Here 3 < 5 , there for we will replace 3 by 0 Ans – 254 Q. Round off to nearest 10. a) 73 b) 145 c) 295 d) 3,244 e) 51,766

19. Rounding off number nearest 100 We replace the digit in tens and ones place by 00. If the tens place is > 5 , we increase the digit in hundreds place by 1, else make nu changes Eg. 25 4 3 Here 4 < 5 , there for we will replace tens and ones place by 00 Ans – 25 00 Eg. 25 6 3 Here 6 > 5 , there for we will replace tens and ones place by 00 and increase hundreds place digit i.e. 5 by 1 Ans – 2 600 Q.Round off to nearest 100 a) 263 b) 1350 c) 4731 d) 5660 e) 32,892

20. Rounding off number nearest 1000 We replace the digit in hundreds ,tens and ones place by 000. If the hundreds digit is > 5 , we increase the digit in thousands place by 1, else make n0 changes Eg. 25 4 30 Here 4 < 5 , there for we will replace hundreds , tens and ones place by 000 Ans – 25 000 Eg. 25 6 30 Here 6 > 5 , there for we will replace hundreds, tens and ones place by 000 and increase thousands place digit i.e. 5 by 1 Ans – 2 600 Q. Round of to nearest 1000 a) 971 b) 3501 c) 8489 d) 29,604 e) 599,512

21. Practice A 3-digit number was rounded off to the nearest hundred and the result was 600. Find the interval of the original number. Solution : Each number from 550 to 599 can be rounded off to 600 Each number from 601 to 649 can be rounded of as 600. So, interval of the original number is 550 to 649

22. Roman Numerals I V X L C D M 1 5 10 50 100 500 1000 There are no roman numerals for 0. When a symbol is repeated , the value of roman number = Value of roman numeral X times it is repeated Eg. I I = 1 X 2 = 2 X X = 10 X 2 = 20 Symbols V , L and D are never repeated. X = 10 and not VV

23. Roman Numerals I V X L C D M 1 5 10 50 100 500 1000 If a numeral is written to right of another symbol of greater value, the value of numbers is sum of value of symbols. Eg. X I = 10 + 1 = 11 V I = 5 + 1 = 6 If a numeral is written to left of another symbol of greater value, the value of numbers is difference of value of symbols. Eg. I X = 10 - 1 = 9 I V = 5 - 1 = 4

24. Roman Numerals I V X L C D M 1 5 10 50 100 500 1000 If symbols are combined, the value of smaller symbol in middle of two greater symbol is subtracted from value of symbol on the right. Eg. X I V = 10 + ( 5 -1) = 14 X X X I X = 10 + 10 + 10 + ( 10 – 1) = 39