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MATHEMATICS WORKSHEET 2014-15 CLASS VI KNOWING OUR NUMBERS - Worksheet discussion 1. The smallest 4 digit number using 2,9,6 & 0 is: a. 6290 b. 2690 c. 0269 d. 2069 2. The difference between place values of 4 in 3,49,406 is: a. 36000 b. 39600 c. 36900 d. 3600 3. In international system, we write 1 million for a. 100000 b. 10000 c. 1000000 d. 10000000 4. Write the following numbers in expanded form and write the number names in Indian and international system of numeration: a. 523680 b. 34512 c. 100579 d. 3982105 a. 5,23,680 = 5x100000 + 2x10000 + 3x1000 + 6x100+ 8x10 Indian system no. name: five lakhs, twenty three thousand, six hundred eighty. International system: five hundred twenty three thousand, six hundred eighty b. 34, 512 = 3x10,000 + 4x1000 + 5x100 + 1x10 +2x1. Number names: Indian system: thirty four thousand, five hundred twelve. International system: thirty four thousand, five hundred twelve c. 1,00,579 = 1x1,00,000 + 5x100 + 7x10 + 9x1 Number Names: Indian system: one lakh, five hundred seventy nine. International system: hundred thousand, five hundred seventy nine. d. 39,82,105 = 3x10,00,000 + 9x1,00,000 + 8x10,000 + 2x1000 + 1x100 + 5x1. Indian system: thirty nine lakh, eighty two thousand, hundred five. International syste,: three million, nine hundred eighty two thousand, hundred five. 5. Place commas correctly and write the numerals: a. Fifty six lakhs thirty two thousands and three 56, 32,003 b. Thirty million two hundred and forty three thousand sixty five 30,243,065 c. Eight crore ninety lakhs twenty three thousand five hundred eighty four 8,90,23,584 Page 1 of 6 d. Two million nine thousand nineteen 2,009,019. 6. Rewrite using Indian place value system a. Four hundred five thousand six hundred ten 4,05,610 - Four lakh five thousand six hundred ten b. Two million five hundred six thousand three hundred fifteen 25,60, 315 - twenty five lakh, sixty thousand, three hundred fifteen c. Eight million two hundred twenty five thousand five hundred four 82,25,504 - eighty two lakh, twenty five thousand, five hundred four. 7. Round off to nearest tens: 46 - 50 388 - 390 4653 - 4650 46, 388, 4653 8. Round off to nearest hundreds: 894 - 900 3281 - 3300 86543 - 86500 894, 3281, 86543 9. Round off to nearest thousands: 465981 - 466000 5498 - 5000 12965 - 13000 465981, 5498, 12965 10. Estimate the following to the nearest hundred and solve a. 8042 + 1355 Rounding off: 8000 + 1400 = 9400 b. 5683 + 2146 + 368 Rounding off: 5700 + 2100 + 400 = c. 7134 - 3658 Rounding off: 7100 - 3700 = d. 7258 – 2429 Rounding off: 7300 - 2400 = e. 264 x 147 Rounding off: 300 x 100 = f. 506 x 179 Rounding off: 500 x 200 = 1,00,000 Page 2 of 6 g. 472 ÷ 76 Rounding off: 500 ÷ 100 = 5 h. 755 ÷ 120 Rounding off: 800 ÷ 100 = 8 11. Round off 4398 & 256 to the nearest tens. Add them and round off the sum to the nearest hundred Rounding off to nearest tens: 4398 -- 4400 256 -- 260 Adding them: 4400 + 260 = 4660 Rounding off the sum to the nearest hundred 4660 -- 4700. 12. Write the following as Hindu-Arabic numerals a. CLIV = 154 b. XCIV = 94 c. CDXIV= 414 d. DCCLXIX=769 e. CCXXIV = 224 f. MCMXLVIII = 1948 g. LIV = 54 h. MDLXXVII = 1577 i. XLIX = 49 J. DCLX=660 13. Simplify the following: a. 96 – { (15 ÷ 3) – (45 ÷ 15) } x 10 + 4 Solution: 96 – { (15 ÷ 3) – (45 ÷ 15) } x 10 + 4 = 96 – {(5)-(3)} x 10 + 4 = 96 – 2 x 10 + 4 = 96 - 20 +4 = 96-24 = 72 b. 120 ÷ [ 18 – { 20 - 3 x (9 – 5) } ] Solution: 120 ÷ [ 18 – { 20 - 3 x (9 – 5) } ] = 120 ÷ [ 18 –{ 20 - 3 x4 } ] = 120 ÷ [ 18 –{20-12}] = 120 ÷ [ 18 –8] =120 ÷ 10 = 12 c. 120 – [132 ÷ (3 x 4) – { 20 – 15 – 3 } ] Solution: 120 – [132 ÷ (3 x 4) – { 20 – 15 – 3 } ] =120 – [132 ÷ (3 x 4) –{5-3}] =120 – [132 ÷12 - 2] = 120 – [11-2] =120 –9 = 111 d. (19 – 6) x [ 19 + { 15 + 8 – 3 } ] Solution: (19 – 6) x [ 19 + { 15 + 8 – 3 } ] Page 3 of 6 =(19 – 6) x [ 19 + {23-3}] = 13 x [19 +20] = 13 x 39 = 507 e. 100 – [ 18 – { 16 ÷ 2 – ( 16 – 12 ÷ 3 ) ÷ 2 } ] Solution: 100 – [ 18 – { 16 ÷ 2 – ( 16 – 12 ÷ 3 ) ÷ 2 } ] =100 – [ 18 – { 16 ÷ 2 – ( 16 –4) ÷ 2 } ] =100 – [ 18 – { 16 ÷ 2 –4÷ 2 } ] =100 – [ 18 – {8 - 2}] = 100 - [ 18 – 6 ] =100 - 12 = 88 f. 90 x [ 143 – { ( 6 × 7 ) + ( 110 – 3 x 8 ) } ] Solution: 90 x [ 143 – { ( 6 × 7 ) + ( 110 – 3 x 8 ) } ] = 90 x [ 143 – {42 + ( 110 – 24) } ] = 90 x [ 143 – {42 + 86}] =90 x [ 143 – 128] =90 x 15 = 1,350 14 .Give a rough estimate (by rounding off to the nearest hundreds and a closer estimste (by rounding off to the nearest tens ) and check with the actual. a) 34768 – 12353 Rough estimate: (rounding off to nearest 100's) 34768 -- 34800 12353 -- 12400 34800 - 12400 = 22400. Closer estimate: (rounding off to nearest 10's) 34768 -- 34770 ; 12353 -- 12360 34770 - 12360 = 22410 Actual estimate: 34768 – 12353 = 22415. b) 90156 – 5679 =rough estimate -84500 =closer estimate – 84480 = actual answer - 84477 c) 1023 + 456 + 385 = rough estimate - 2400 =closer estimate - 1870 Page 4 of 6 = actual answer - 1864 Answer the following 1. How many seven digit numbers are there in all? Solution: Smallest 7 digit number = 10,00,000 Biggest 7 digit number = 99, 99, 999 Total number of seven digit numbers = (99,99,999 - 10,00,000) + 1 = 9, 000, 000. 2. How many millions are there in one crore? 10 millions are there in 1 crore. 3. How many thousands make a lakh? 100 thousands. 4. What comes just after 95479999? 95,480,000 5. Write the smallest eight digit number having four different digits. 10,001,123 6. Write all three digit numbers using the digits 1, 3, 5 taking each digit only once and arrange them in descending order. 135, 315, 513, 531, 153, 351 Descending order: 531, 513, 351, 315, 153, 135 7. Find the difference between the number 1738 and that obtained on reversing its digits. Reversing the number: 8371 Difference : 8371 - 1738 = 6633. 8. Find the difference between the place values of two 9s in 7,95,20,986 Difference in Place value: 90,00,000 - 900 = 8,999,100 9. What comes just before 9,900,000 Ans: 9,899,999 10. The difference between 2 numbers is 9476583. If the smaller is 6873547, find the greater one. Solution: Difference btween two numbers = 9476583 Smallest no. = 6873547 Another no. = 9,476,583 + 6,873,547 = 16,350,130 11. A number exceeds 3,76,84,955 by 36,15,045. What is that number? solution: 3,76,84,955 + 36,15,045 = 41,300,000 12. By how much is 7,32,46,510 larger than 4,65,86,422? 7,32,46,510 - 4,65,86,422 = 26,660,088 13. The cost of 16 flats constructed by a builder is ₹ 2,48,09,520. What is the cost of each flat? ans: 2,48,09,520 ÷ 16 = 1,550,595 14. Mr. Baskar saves ₹ 8756 every month. How much money will he save in 13 years? Ans: 8756 x 12 x13 = 1,365,936 Page 5 of 6 15. A textile mill produced 2, 75, 576 m of cloth in a week. Find the daily production of the mill. Ans: 2, 75, 576 ÷ 7 = 39,368. ___________________________________________________________ Page 6 of 6