Class 6 Whole Numbers Exercise 3.1-2

\begin{array}{l} \text {Q11. Fill in the blanks with the appropriate symbol } \lt \text { or } \gt : \\ (i) \quad 25 \ldots 205 \quad (ii) \quad 170 \ldots 107 \quad (iii) \quad 415 \ldots 514 \\ (iv) \quad 10001 \ldots 100001 \quad (v) \quad 2300014 \ldots 2300041 \\ \\\text {Sol. (i) } \quad 25 \lt 205 \\ \text {(ii) } \quad 170 \gt 107 \\ \text {(iii) } \quad 415 \lt 514 \\ \text {(iv) } \quad 10001 \lt 100001 \\ \text {(v) } \quad 2300014 \lt 2300041 \\ \\\text {Q12. Arrange the following numbers in descending order: } \\ 925,786,1100,141,325,886,0,270 \\ \\\text {Sol. Numbers in descending order is as follows: } \\ 1100,925,886,786,325,270,141,0 \\ \\\text {Q13. Write the largest number of 6 digits and the smallest number of 7 digits. } \\ \text { Which one of these two is larger and by how much? } \\ \\\text {Sol. 999999 is the largest number of 6 digits.} \\ \text {And 1000000 is the smallest number of 7 digits.} \\ \text {1000000 is larger than 999999 by 1.} \\ \\\text {Q14. Write down three consecutive whole numbers just preceding 8510001 } \\ \\\text {Sol. The three consecutive whole numbers just preceding 8510001 are } \\ 8510001- 1 = 8510000 \\ 8510001- 2 = 8509999 \\ 8510001- 3 = 8509998 \\ \\\text {Q15. Write down the next three consecutive whole numbers starting from 4009998 } \\ \\\text {Sol. The next three consecutive whole numbers starting from 4009998 are } \\ 4009998 + 1 = 4009999 \\ 4009998 + 2 = 4010000 \\ 4009998 + 3 = 4010001 \\ \\\text {Q16. Give arguments in support of the statement that there does not exist the largest natural number. } \\ \\\text {Sol. Every natural number has its successor.} \\ \\\text {Q17. Which of the following statements are true and which are false? } \\ \text {(i) Every whole number has its successor. } \\ \text {(ii) Every whole number has its predecessor.} \\ \text {(iii) 0 is the smallest natural number.} \\ \text {(iv) 1 is the smallest whole number.} \\ \text {(v) 0 is less than every natural number.} \\ \text {(vi) Between any two whole numbers there is a whole number.} \\ \text {(vii) Between any two non-consecutive whole numbers there is a whole number.} \\ \text {(viii) The smallest 5 -digit number is the successor of the largest 4 digit number.} \\ \text {(ix) Of the given two natural numbers, the one having more digits is greater.} \\ \text {(x) The predecessor of a two digit number cannot be a single digit number.} \\ \text {(xi) If a and b are natural numbers and } a \lt b \text {, than there is a natural number c such that } a \lt c \lt b \\ \text {(xii) If a and b are whole numbers and } a \lt b\text {, then } a+1 \lt b+1 \\ \text {(xiii) The whole number 1 has 0 as predecessor. } \\ \text {(xiv) The natural number 1 has no predecessor. } \\ \\\text {Sol. (i) True. For example the successor of 0 is 1, successor of 1 is 2, successor of 2 is 3 and so on. } \\\text {(ii) False. Every whole number does not have any predecessor.} \\ \text {(iii) False. 0 is not the smallest natural number. } \\ \text {(iv) False. 1 is not the smallest whole number. } \\ \text {(v) True. 0 is less than natural numbers 1,2,3,4,5 and so on. } \\ \text {(vi) False. There is no whole number between two whole numbers.} \\ \text {(vii) True. Whole number exists between two consecutive whole numbers. } \\ \text {(viii) True. For example, 10000 is the successor of 9999 } \\ \text {(ix) True. For example, 100 is greater than 99 } \\ \text {(x) False. For example, the predecessor of 100 is 99.} \\ \text {(xi) False. Example: Natural numbers } 99 \lt 100 \gt 98 \\ \text {(xii) True. It means that } 1+2 \lt 3+1 \text { i.e.} 3 \lt 4 \\ \text {(xiii) True. We know that } 1 \gt 0 \\ \text {(xiv)True. Natural number starts from 1,2,3 and so on. } \\ \therefore \text {The natural number 1 has no predecessor.} \\ \\ \end{array}